Physics 10(2)- Simple Harmonic Motion and Waves PDF

Unit 10 SIMPLE HARMONIC MOTION AND WAVES After studying this unit, students will be able to: state the conditions necessary for an object to oscillate with SHM. explain SHM with simple pendulum, ball and bowl examples. draw forces acting on a displaced pendulum. solve problems...

Unit 10 SIMPLE HARMONIC MOTION AND WAVES After studying this unit, students will be able to: state the conditions necessary for an object to oscillate with SHM. explain SHM with simple pendulum, ball and bowl examples. draw forces acting on a displaced pendulum. solve problems by using the formula T = 2π ll l /g g for simple pendulum. understand that damping progressively reduces the amplitude of oscillation. describe wave motion as illustrated by vibrations in rope, slinky spring and by experiments with water waves. describe that waves are means of energy transfer without transfer of matter. distinguish between mechanical and electromagnetic waves. identify transverse and longitudinal waves in mechanical media, slinky and springs. define the terms speed (v), frequency ( f ), wavelength (λ), time period (T ), amplitude, crest, trough, cycle, wavefront, compression and rarefaction. derive equation v = f λ. solve problems by applying the relation f = 1/T and v = f λ. describe properties of waves such as reflection, refraction and diffraction with the help of ripple tank. Science, Technology and Society Connections The students will be able to: explain the diffraction of radiowaves but not of T.V waves (transmission can be heard in such areas where the waves cannot reach directly). SIMPLE HARMONIC MOTION AND WAVES A body is said to be vibrating if it moves back and forth or to For your information and fro about a point. Another term for vibration is oscillation. A special kind of vibratory or oscillatory motion is called the simple harmonic motion (SHM), which is the main focus of this chapter. We will discuss important characteristics of SHM and systems executing SHM. We will also introduce different types of waves and will demonstrate their properties with the help of ripple tank. A spider detects its prey due to vibration produced in the web. 10.1 SIMPLE HARMONIC MOTION (SHM) In the following sections we will discuss simple harmonic motion of different systems. The motion of mass attached to a spring on a horizontal frictionless surface, the motion of a ball placed in a bowl and the motion of a bob attached to a string are examples of SHM. MOTION OF MASS ATTACHED TO A SPRING One of the simplest types of oscillatory motion is that of horizontal mass-spring system (Fig.10.1). If the spring is stretched or compressed through a small displacement x from its mean position, it exerts a force F on the mass. F=0 According to Hooke’s law this force is directly proportional to the change in length x of the spring i.e., x (a) B O A F=-kx........ (10.1) x=0 F where x is the displacement of the mass from its mean position O, and k is a constant called the spring constant defined as (b) k=- F x x The value of k is a measure of the stiffness of the spring. Stiff F springs have large value of k and soft springs have small value of k. (c) x As F = ma B O A Therefore, k = - ma Fig.10.1: SHM of a mass-spring x system or a=- k x m a  - x........ (10.2) It means that the acceleration of a mass attached to a spring is directly proportional to its displacement from the mean position. Hence, the horizontal motion of a mass-spring system is an example of simple harmonic motion. Not For Sale – PESRP 2 SIMPLE HARMONIC MOTION AND WAVES The negative sign in Eq. 10.1 means that the force exerted by the spring is always directed opposite to the displacement of the mass. Because the spring force always acts towards the mean position, it is sometimes called a restoring force. A restoring force always pushes or pulls the object performing oscillatory motion towards the mean position. For your information Initially the mass m is at rest in mean position O and the x = -A x = 0 x = +A resultant force on the mass is zero (Fig.10.1-a). Suppose the mass is pulled through a distance x up to extreme position A and then released (Fig.10.1-b). The restoring force exerted by the spring on the mass will pull it K.E =0 K.E = max P.E = max K.E = 0 towards the mean position O. Due to the restoring force P.E = 0 P.E = max the mass moves back, towards the mean position O. The Kinetic and potential energy at magnitude of the restoring force decreases with the different positions in a distance from the mean position and becomes zero at O. mass–spring system. However, the mass gains speed as it moves towards the mean position and its speed becomes maximum at O. Due to inertia the mass does not stop at the mean position O but continues its motion and reaches the extreme position B. As the mass moves from the mean position O to the extreme position B, the restoring force acting on it towards the mean position steadily increases in strength. Hence the speed of the mass decreases as it moves towards the extreme position Tidbits B. The mass finally comes briefly to rest at the extreme A human eardrum can oscillate position B (Fig. 10.1-c). Ultimately the mass returns to the back and forth up to 20,000 mean position due to the restoring force. times in one second. This process is repeated, and the mass continues to oscillate back and forth about the mean position O. Such motion of a mass attached to a spring on a horizontal frictionless surface is known as Simple Harmonic Motion (SHM). Quick Quiz The time period T of the simple harmonic motion of a mass What is the displacement of an ‘m’ attached to a spring is given by the following equation: object in SHM when the kinetic and potential energies are m......... (10.3) equal? T  2 k´ 3 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES BALL AND BOWL SYSTEM The motion of a ball placed in a bowl is another example of B Ball A simple harmonic motion (Fig 10.2). When the ball is at the R mean position O, that is, at the centre of the bowl, net force acting on the ball is zero. In this position, weight of the ball acts downward and is equal to the upward normal force of O Bowl the surface of the bowl. Hence there is no motion. Now if we w = mg bring the ball to position A and then release it, the ball will Fig. 10.2: When a ball is gently start moving towards the mean position O due to the displaced from the centre of a restoring force caused by its weight. At position O the ball bowl it starts oscillating about gets maximum speed and due to inertia it moves towards the the centre due to force of gravity which acts as a extreme position B. While going towards the position B, the restoring force speed of the ball decreases due to the restoring force which acts towards the mean position. At the position B, the ball stops for a while and then again moves towards the mean position O under the action of the restoring force. This to and fro motion of the ball continues about the mean position O till all its energy is lost due to friction. Thus the to and fro motion of the ball about a mean position placed in a bowl is an example of simple harmonic motion. MOTION OF A SIMPLE PENDULUM A simple pendulum also exhibits SHM. It consists of a small θ bob of mass ‘m’ suspended from a light string of length ‘ l ’ T T fixed at its upper end. In the equilibrium position O, the net l force on the bob is zero and the bob is stationary. Now if we T B bring the bob to extreme position A, the net force is not zero A m S m (Fig.10.3). There is no force acting along the string as the o m mgsinθ tension in the string cancels the component of the weight mg mgcosθ mg cos θ. Hence there is no motion along this direction. w = mg The component of the weight mg sin θ is directed towards the Mean position mean position and acts as a restoring force. Due to this force Fig. 10.3: Forces acting on a the bob starts moving towards the mean position O. At O, the displaced pendulum. The bob has got the maximum velocity and due to inertia, it does restoring force that causes the not stop at O rather it continues to move towards the pendulum to undergo simple extreme position B. During its motion towards point B, the harmonic motion is the component of gravitational velocity of the bob decreases due to restoring force. The force mg sinθ tangent to the velocity of the bob becomes zero as it reaches the point B. path of motion Not For Sale – PESRP 4 SIMPLE HARMONIC MOTION AND WAVES The restoring force mgsinθ still acts towards the mean position O and due to this force the bob again starts moving towards the mean position O. In this way, the bob continues its to and fro motion about the mean position O. Time Period It is clear from the above discussion that the speed of the bob increases while moving from point A to O due to the restoring force which acts towards O. Therefore, acceleration of the bob is also directed towards O. Similarly, when the bob moves from O to B, its speed decreases due to restoring force which again acts towards O. Therefore, acceleration of the bob is again directed towards O. It follows that the acceleration of the bob is always directed towards the mean position O. Hence the motion of a simple pendulum is SHM. We have the following formula for the time period of a simple pendulum Time period of a pendulum is the time to complete one ll......... (10.4) cycle. T  2 ß g From the motion of these simple systems, we can define SHM as: For your information Simple harmonic motion occurs when the net force is The period of a pendulum is directly proportional to the displacement from the mean independent of its mass and position and is always directed towards the mean amplitude. position. In other words, when an object oscillates about a fixed position (mean position) such that its acceleration is directly proportional to its displacement from the mean position and is always directed towards the mean position, its motion is Check Your Understanding called SHM. Tell whether or not these motions are examples of simple harmonic motion: Important features of SHM are summarized as: (a) up and down motion of a i. A body executing SHM always vibrates about a fixed leaf in water pond (b) motion position. of a ceiling fan (c) motion of ii. Its acceleration is always directed towards the mean hands of clock (d) motion of a position. plucked string fixed at both its ends (e) movement of honey iii. The magnitude of acceleration is always directly bee. proportional to its displacement from the mean 5 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES position i.e., acceleration will be zero at the mean position while it will be maximum at the extreme positions. iv. Its velocity is maximum at the mean position and zero at the extreme positions. Now we discuss different terms which characterize simple harmonic motion. Vibration: One complete round trip of a vibrating body about its mean position is called one vibration. Time Period (T ): The time taken by a vibrating body to complete one vibration is called time period. Frequency ( f ): The number of vibrations or cycles of a For your information vibrating body in one second is called its frequency. It is reciprocal of time period i.e., f = 1/T Amplitude (A): The maximum displacement of a vibrating body on either side from its mean position is called its amplitude. Example 10.1: Find the time period and frequency of a simple pendulum 1.0 m long at a location where g = 10.0 m s-2. Christian Huygens invented Solution: Given, l = 1.0 m, g = 10.0 m s. -2 the pendulum clock in 1656. He was inspired by the work of Using the formula, Galileo who had discovered T  2 l gßg that all pendulums of the same length took the same amount By putting the values of time to complete one full swing. Huygens developed the 1.0 m first clock that could accurately T  2 3.14  T = 1.99 s 10.0 m ss2 measure time. Frequency of simple pendulum is given by f = 1/T = 1/1.99 s = 0.50 Hz 10.2 DAMPED OSCILLATIONS Vibratory motion of ideal systems in the absence of any friction or resistance continues indefinitely under the action of a restoring force. Practically, in all systems, the force of friction retards the motion, so the systems do not oscillate indefinitely. The friction reduces the mechanical energy of Not For Sale – PESRP 6 SIMPLE HARMONIC MOTION AND WAVES the system as time passes, and the motion is said to be Displacement + Decreasing damped. This damping progressively reduces the amplitude amplitide of the vibration of motion as shown in Fig. 10.4. o Time Shock absorbers in automobiles are one practical application “Envelope” of of damped motion. A shock absorber consists of a piston - the damping Fig. 10.4: The variation of moving through a liquid such as oil (Fig.10.5). The upper part amplitude with time of of the shock absorber is firmly attached to the body of the car. damping system When the car travels over a bump on the road, the car may vibrate violently. The shock absorbers damp these vibrations and convert their energy into heat energy of the oil. Thus Attached to car frame The oscillations of a system in the presence of some resistive force are damped oscillations. Piston Liquid 10.3 WAVE MOTION Attached to car axle Waves play an important role in our daily life. It is because Fig. 10.5: Shock absorber waves are carrier of energy and information over large distances. Waves require some oscillating or vibrating source. Pencil Here we demonstrate the production and propagation of different waves with the help of vibratory motion of objects. Activity 10.1: Dip one end of a pencil into a tub of water, and move it up and down vertically (Fig. 10.6). The disturbance in Cork the form of ripples produces water waves, which move away from the source. When the wave reaches a small piece of cork floating near the disturbance, it moves up and down about its Fig. 10.6: Waves produced by dipping a pencil in a water tub original position while the wave will travel outwards. The net Support displacement of the cork is zero. The cork repeats its P vibratory motion about its mean position. Crest Activity 10.2: Take a rope and mark a point P on it. Tie one P end of the rope with a support and stretch the rope by P holding its other end in your hand (Fig. 10.7). Now, flipping the rope up and down regularly will set up a wave in the rope which will travel towards the fixed end. The point P on the rope will start vibrating up and down as the wave passes P Trough across it. The motion of point P will be perpendicular to the Fig. 10.7: Waves produced in a direction of the motion of wave. rope 7 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES From the above simple activities, we can define wave as: For your information A wave is a disturbance in the medium which causes Electric field the particles of the medium to undergo vibratory Magnetic field motion about their mean position in equal intervals of time. There are two categories of waves: Direction of wave motion 1. Mechanical waves Electromagnetic waves consist 2. Electromagnetic waves of electric and magnetic fields oscillating perpendicular to Mechanical Waves: Waves which require any medium for each other. their propagation are called mechanical waves. Examples of mechanical waves are water waves, sound waves and waves produced on the strings and springs. Quick Quiz Do mechanical waves pass Electromagnetic Waves: Waves which do not require any through vacuum, that is, empty space? medium for their propagation are called electromagnetic waves. Radiowaves, television waves, X-rays, heat and light waves are some examples of electromagnetic waves. 10.4 TYPES OF MECHANICAL WAVES Depending upon the direction of displacement of medium with respect to the direction of the propagation of wave itself, mechanical waves may be classified as longitudinal or transverse. Longitudinal waves can be produced on a spring (slinky) placed on a smooth floor or a long bench. Fix one end of the slinky with a rigid support and hold the other end into your hand. Now give it a regular push and pull quickly in the direction of its length (Fig.10.8). Not For Sale – PESRP 8 SIMPLE HARMONIC MOTION AND WAVES Movement of hand Support Direction of wave travel Displacement of particles Compression λ For your Information Compression Rarefaction Compression Longitudinal waves move Fig. 10.8: Longitudinal wave on a slinky Fig. 10.8: Longitudinal wave on a slinky faster through solids than through gases or liquids. A series of disturbances in the form of waves will start moving Tra n sve rs e wave s m o ve along the length of the slinky. Such a wave consists of regions through solids at a speed of called compressions, where the loops of the spring are close less than half of the speed of together, alternating with regions called rarefactions longitudinal waves. It is (expansions), where the loops are spaced apart. In the regions of because the restoring force exerted during this up and compression, particles of the medium are closer together while down motion of particles of in the regions of rarefaction, particles of the medium are spaced the medium is less than the apart. The distance between two consecutive compressions is restoring force exerted by a called wavelength. The compressions and rarefactions move back and forth motion of back and forth along the direction of motion of the wave. Such a particles of the medium in case of longitudinal waves. wave is called longitudinal wave and is defined as: In longitudinal waves the particles of the medium move back and forth along the direction of propagation of wave. We can produce transverse waves with the help of a slinky. Stretch out a slinky along a smooth floor with one end fixed. Grasp the other end of the slinky and move it up and down quickly (Fig.10.9). A wave in the form of alternate crests and troughs will start travelling towards the fixed end. The crests are the highest points while the troughs are the lowest points of the particles of the medium from the mean position. The distance between two consecutive crests or troughs is called 9 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES wavelength. The crests and troughs move perpendicular to the direction of the wave. λ Wave movement Crest Particle movement Movement of hand Support from side to side Troughs Fig. 10.9: Transverse wave on a slinky Therefore, transverse waves can be defined as: In case of transverse waves, the vibratory motion of particles of the medium is perpendicular to the direction of propagation of waves. Waves on the surface of water and light waves are examples of transverse waves. WAVES AS CARRIERS OF ENERGY Energy can be transferred from one place to another through waves. For example, when we shake the stretched string up and down, we provide our muscular energy to the string. As a result, a set of waves can be seen travelling along the string. The vibrating force from the hand disturbs the particles of the string and sets them in motion. These particles then transfer their energy to the adjacent particles in the string. Energy is thus transferred from one place of the medium to the other in the form of wave. The amount of energy carried by the wave depends on the distance of the stretched string from its rest position. That is, the energy in a wave depends on the amplitude of the wave. If we shake the string faster, we give more energy per second to produce wave of higher frequency, and the wave delivers more energy per second to the particles of the string as it moves forward. Water waves also transfer energy from one place to another Not For Sale – PESRP 10 SIMPLE HARMONIC MOTION AND WAVES as explained below: Activity 10.3: Drop a stone into a pond of water. Water waves will be produced on the surface of water and will travel outwards (Fig. 10.10). Place a cork at some distance from the falling stone. When waves reach the cork, it will move up and down alongwith the motion of the water particles by getting For your information energy from the waves. Generating a high frequency wave, requires more energy per second than to generate a low frequency wave. Thus, a high frequency wave carries more energy than a low frequency wave of the same amplitude. Cork and water go up and down Energy travels in this direction Fig. 10.10 This activity shows that water waves like other waves transfer energy from one place to another without transferring matter, i.e., water. RELATION BETWEEN VELOCITY, FREQUENCY AND Do you know? WAVELENGTH Earthquake produces waves Wave is a disturbance in a medium which travels from one through the crust of the Earth place to another and hence has a specific velocity of travelling. in the form of seismic waves. By studying such waves, the This is called the velocity of wave which is defined by geophysicists learn about the Velocity = distance/time internal structure of the Earth v = d and information about the t occurrence of future Earth If time taken by the wave in moving from one point to another activity. is equal to its time period T, then the distance covered by the wave will be equal to one wavelength λ, hence we can write: v = λ T 1 But time period T, is reciprocal of the frequency f, i.e., T  f 11 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES Therefore, v =f λ......... (10.5) Eq. (10.5) is true both for longitudinal and transverse waves. Example 10.2: A wave moves on a slinky with frequency of 4 Hz and wavelength of 0.4 m. What is the speed of the wave? Solution: Given that, f = 4 Hz, λ = 0.4 m Wave speed v =f λ = (4 Hz) (0.4 m) v = 1.6 m s-1 10.5 RIPPLE TANK Ripple tank is a device to produce water waves and to study their characteristics. This apparatus consists of a rectangular tray having glass bottom and is placed nearly half metre above the surface of a table (Fig. 10.11). Waves can be produced on the surface of water present in the tray by means of a vibrator (paddle). Lamp Power supply Shallow tank of water Oscillating paddle Wave patterns on a viewing screen Fig. 10.11: Ripple tank apparatus λ This vibrator is an oscillating electric motor fixed on a wooden plate over the tray such that its lower surface just touches the surface of water. On setting the vibrator ON, this wooden plate starts vibrating to generate water waves consisting of straight wavefronts (Fig.10.12). An electric bulb is hung above the tray to observe the image of water waves on the Fig. 10.12: Waves consisting of paper or screen. The crests and troughs of the waves appear straight wavefronts as bright and dark lines respectively, on the screen. Now we explain the reflection of water waves with the help of ripple tank. Not For Sale – PESRP 12 SIMPLE HARMONIC MOTION AND WAVES Place a barrier in the ripple tank. The water waves will reflect Quick Quiz from the barrier. If the barrier is placed at an angle to the What do the dark and bright fringes on the screen of ripple wavefront, the reflected waves can be seen to obey the law of tank represent? reflection i.e., the angle of the incident wave along the normal will be equal to the angle of the reflected wave Angle of (Fig.10.13). Thus, we define reflection of waves as: incidence When waves moving in one medium fall on the surface of Normal another medium they bounce back into the first medium such Incident i Barrier waves that the angle of incidence is equal to the angle of reflection. (a) The speed of a wave in water depends on the depth of water. If a block is submerged in the ripple tank, the depth of water in the tank will be shallower over the block than elsewhere. Normal Angle of When water waves enter the region of shallow water their reflection r wavelength decreases (Fig.10.14). But the frequency of the water waves remains the same in both parts of water Barrier because it is equal to the frequency of the vibrator. (b) λ2 Shallow water Reflected waves Boundary between (slow speed) Fig. 10.13: Reflection of water v2 waves from a plane barrier deep and Wavefront shallow water Deep water Straight wave λ1 v1 (faster speed) generator Ripple tank Fig. 10.14 For the observation of refraction of water waves, we repeat the above experiment such that the boundary between the deep and the shallower water is at some angle to the wavefront (Fig. 10.15). Now we will observe i that in addition to the change in wavelength, the waves change their direction of propagation as well. Note that i r the direction of propagation is always normal to the wavefronts. This change of path of water waves while r passing from a region of deep water to that of shallower Fig. 10.15: Refraction of water one is called refraction which is defined as: waves 13 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES When a wave from one medium enters into the second medium at some angle, its direction of travel changes. Now we observe the phenomenon of diffraction of water waves. Generate straight waves in a ripple tank and place two obstacles in line in such a way that separation between them is equal to the wavelength of water waves. After passing through a small slit between the two obstacles, the waves will spread in every direction and change into almost semicircular pattern (Fig. 10.16). Diffraction of waves can only be observed clearly if the size of the obstacle is comparable with the wavelength of the wave. Fig.10.16: Diffraction of water Fig.10.17 shows the diffraction of waves while passing through waves through a small slit a slit with size larger than the wavelength of the wave. Only a small diffraction occurs near the corners of the obstacle. The bending or spreading of waves around the sharp edges or corners of obstacles or slits is called diffraction. Example 10.3: A student performs an experiment with waves in water. The student measures the wavelength of a wave to be 10 cm. By using a stopwatch and observing the oscillations Fig.10.17: Diffraction of water of a floating ball, the student measures a frequency of 2 Hz. If waves through a large slit the student starts a wave in one part of a tank of water, how long will it take the wave to reach the opposite side of the Deep tank 2 m away? Solution: Shallow (1) We are given the frequency, wavelength, and distance. (2) We have to calculate the time, the wave takes to move a Fig.10.18 distance of 2 m. (3) The relationship between frequency, wavelength, and speed is ACTIVITY v = f λ. The relationship between time, speed, and distance is Study Fig. 10.18 to answer the v = d /t following questions: (4) Rearrange the speed formula to solve for the time: t = d / v 1. What happens to the direction of wave when water The speed of the wave is the frequency times the wavelength. waves pass from deep to v = f λ = (2 Hz)(0.1 m) = 0.2 m s-1. shallow part of the water? Use this value to calculate the time: 2. Are the magnitudes of angle t = 2 m/0.2 m s-1 = 10 s of incidence and angle of refraction equal? 3. Which will be greater? Not For Sale – PESRP 14 SIMPLE HARMONIC MOTION AND WAVES SUMMARY  Simple harmonic motion (SHM) is a to and fro oscillatory motion in which acceleration of the body is directly proportional to the displacement of the body from the mean position and is always directed towards the mean position.  The motion of a mass attached to a spring, simple pendulum and that of a ball inside a bowl is SHM.  Time taken by the simple pendulum to complete one cycle is called its time period. It depends upon the length of the pendulum and is independent of the mass and amplitude of the pendulum.  The number of cycles completed in one second is called frequency of a vibrating body. It is reciprocal of time period.  The maximum displacement from mean position of a body performing SHM is called amplitude.  Wave is a phenomenon of transferring energy from one place to another without the transfer of matter.  Mechanical waves are those waves which require some medium for their propagation.  Electromagnetic waves do not require any medium for their propagation.  Transverse waves are the mechanical waves in which particles of the medium vibrate about their mean position perpendicular to the direction of propagation of the waves.  Compressional (longitudinal) waves are the mechanical waves in which particles of the medium vibrate about their mean position along the direction of propagation of the waves.  The speed (v) of a wave is equal to the product of frequency ( f ) and wavelength (λ) i.e.,v =f λ.  Ripple tank is a device used to produce water waves and to demonstrate different properties of water waves like reflection, refraction and diffraction.  When a wave travelling from one medium falls on the surface of another medium, it may bounce back into the first medium. This phenomenon is called reflection of waves.  When waves from one medium enter the second medium at some angle their direction of travel may change. This phenomenon is called refraction of waves. The speed and wavelength of wave change in different media but frequency does not change.  The bending of waves around obstacles or sharp edges is called diffraction of waves. 15 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES MULTIPLE CHOICE QUESTIONS Choose the correct answer from the following choices: i. Which of the following is an example of simple harmonic motion? (a) the motion of simple pendulum (b) the motion of ceiling fan (c) the spinning of the Earth on its axis (d) a bouncing ball on a floor ii. If the mass of the bob of a pendulum is increased by a factor of 3, the period of the pendulum's motion will (a) be increased by a factor of 2 (b) remain the same (c) be decreased by a factor of 2 (d) be decreased by a factor of 4 iii. Which of the following devices can be used to produce both transverse and longitudinal waves? (a) a string (b) a ripple tank (c) a helical spring (slinky) (d) a tuning fork iv. Waves transfer (a) energy (b) frequency (c) wavelength (d) velocity v. Which of the following is a method of energy transfer? (a) conduction (b) radiation (c) wave motion (d) all of these vi. In a vacuum, all electromagnetic waves have the same (a) speed (b) frequency (c) amplitude (d) wavelength vii. A large ripple tank with a vibrator working at a frequency of 30 Hz produces 25 complete waves in a distance of 50 cm. The velocity of the wave is -1 -1 (a) 53 cm s (b) 60 cm s -1 -1 (c) 750 cm s (d) 1500 cm s viii. Which of the following characteristics of a wave is independent of the others? (a) speed (b) frequency (c) amplitude (d) wavelength ix. The relation between v, f and λ of a wave is (a) v f = λ (b) f λ = v (c) v λ = f (d) v = λ / f Not For Sale – PESRP 16 SIMPLE HARMONIC MOTION AND WAVES REVIEW QUESTIONS 10.1. What is simple harmonic motion? What are the necessary conditions for a body to execute simple harmonic motion? 10.2. Think of several examples of motion in everyday life that are simple harmonic. 10.3. What are damped oscillations. How damping progressively reduces the amplitude of oscillation? 10.4. How can you define the term wave? Elaborate the difference between mechanical and electromagnetic waves. Give examples of each. 10.5. Distinguish between longitudinal and transverse waves with suitable examples. 10.6. Draw a transverse wave with an amplitude of 2 cm and a wavelength of 4 cm. Label a crest and trough on the wave. 10.7. Derive a relationship between velocity, frequency and wavelength of a wave. Write a formula relating velocity of a wave to its time period and wavelength. 10.8. Waves are the means of energy transfer without transfer of matter. Justify this statement with the help of a simple experiment. 10.9. Explain the following properties of waves with reference to ripple tank experiment: a. Reflection b. Refraction c. Diffraction 10.10. Does increasing the frequency of a wave also increase its wavelength? If not, how are these quantities related? CONCEPTUAL QUESTIONS 10.1. If the length of a simple pendulum is doubled, what will be the change in its time period? 10.2. A ball is dropped from a certain height onto the floor and keeps bouncing. Is the motion of the ball simple harmonic? Explain. 10.3. A student performed two experiments with a simple pendulum. He/She used two bobs of different masses by keeping other parameters constant. To his/her astonishment the time period of the pendulum did not change! Why? 10.4. What types of waves do not require any material medium for their propagation? 10.5. Plane waves in the ripple tank undergo refraction when they move from deep to shallow water. What change occurs in the speed of the waves? NUMERICAL PROBLEMS 10.1. The time period of a simple pendulum is 2 s. What will be its length on the Earth? -2 What will be its length on the Moon if gm =ge/6? where ge = 10 m s. Ans.(1.02 m, 0.17 m) 10.2. A pendulum of length 0.99 m is taken to the Moon by an astronaut. The period of the pendulum is 4.9 s. What is the value of g on the surface of the Moon? 17 Not For Sale – PESRP SIMPLE HARMONIC MOTION AND WAVES Ans.(1.63 m s-2) 10.3. Find the time periods of a simple pendulum of 1 metre length, placed on Earth and th on Moon. The value of g on the surface of Moon is 1/6 of its value on Earth, -2 where ge is 10 m s. Ans.(2 s, 4.9 s) 10.4. A simple pendulum completes one vibration in two seconds. Calculate its length, -2 when g = 10.0 m s. Ans. (1.02 m) 10.5. If 100 waves pass through a point of a medium in 20 seconds, what is the frequency and the time period of the wave? If its wavelength is 6 cm, calculate the wave speed. -1 Ans. (5 Hz, 0.2 s, 0.3 m s ) 10.6. A wooden bar vibrating into the water surface in a ripple tank has a frequency of 12 Hz. The resulting wave has a wavelength of 3 cm. What is the speed of the wave? -1 Ans. (0.36 m s ) 10.7. A transverse wave produced on a spring has a frequency of 190 Hz and travels along the length of the spring of 90 m, in 0.5 s. (a) What is the period of the wave? (b) What is the speed of the wave? (c) What is the wavelength of the wave? -1 Ans. (0.01 s, 180 m s , 0.95 m) 10.8. Water waves in a shallow dish are 6.0 cm long. At one point, the water moves up and down at a rate of 4.8 oscillations per second. (a) What is the speed of the water waves? (b) What is the period of the water waves? -1 Ans. (0.29 m s , 0.21 s) 10.9. At one end of a ripple tank 80 cm across, a 5 Hz vibrator produces waves whose wavelength is 40 mm. Find the time the waves need to cross the tank. Ans. (4 s) 10.10. What is the wavelength of the radiowaves transmitted by an FM station at 90 MHz? 6 8 -1 where 1M = 10 , and speed of radiowave is 3 x 10 m s. Ans. (3.33 m) Not For Sale – PESRP 18  Unit 11 SOUND After studying this unit, students will be able to: explain how sound is produced by vibrating sources and that sound waves require a material medium for their propagation. describe the longitudinal nature of sound waves (as a series of compressions and rarefactions). define the terms pitch, loudness and quality of sound. describe the effect of change in amplitude on loudness and the effect of change in frequency on pitch of sound. define intensity and state its SI unit. describe what is meant by intensity level and give its unit. explain that noise is a nuisance. describe how reflection of sound may produce echo. describe audible frequency range. describe the importance of acoustic protection. solve problems based on mathematical relations learnt in this unit. Science, Technology and Society Connections The students will be able to: describe that some sounds are injurious to health. describe how knowledge of the properties of sound waves is applied in the design of building with respect to acoustics. describe how ultrasound techniques are used in medical and industry. explain the use of soft materials to reduce echo sounding in classroom studies, and other public gathering buildings. SOUND We know that vibrations of objects in any medium produce Physics of Sound All sounds are produced by the waves. For example, vibrator of ripple tank produces water vibrations of objects. Sound is waves. The medium in this case is liquid, but it can also be a a form of energy that travels in gas or a solid. Now we will discuss another type of waves that the form of waves from one we can hear i.e., sound waves. place to another. For your information 11.1 SOUND WAVES Like other waves, sound is also produced by vibrating bodies. Due to vibrations of bodies the air around them also vibrates and the air vibrations produce sensation of sound in our ear. For example, in a guitar, sound is produced due to the vibrations of its strings (Fig. 11.1). Our voice results from the vibrations of our vocal chords. Human heart beats and vibrations of other organs like lungs also produce sound Stethoscopes operate on the waves. Doctors use stethoscope to hear this sound. transmission of sound from the chest-piece, via air-filled hollow tubes, to the listener's Sound waves Ear ears. The chest-piece usually Strings consists of a plastic disc called diaphragm. If the diaphragm is placed on the patient’s body sounds vibrate the diaphragm, creating acoustic pressure Guitar waves which after multiple reflection travel up the tubing Fig. 11.1: Vibrations of guitar strings produce sound waves to the doctor's ears. SOUND IS PRODUCED BY A VIBRATING BODY Rubber hammer Activity 11.1: In school laboratories, we use a device called tuning fork to produce a particular sound. If we strike the tuning fork against rubber hammer, the tuning fork will begin to vibrate (Fig. 11.2). We can hear the Tuning fork sound produced by tuning fork by bringing it near our Fig. 11.2: Strike a rubber ear. We can also feel the vibrations by slightly touching hammer on a tuning fork one of the prongs of the vibrating tuning fork with a plastic ball suspended from a thread (Fig. 11.3). Touch Not For Sale – PESRP 20 SOUND the ball gently with the prong of a vibrating tuning fork. The tuning fork will push the ball because of its Thread vibrations. Now if we dip the vibrating tuning fork into a glass of water, we will see a splash (Fig. 11.4). What does Table tennis make the water splash? ball From this activity, we can conclude that sound is produced by Vibrating vibrating bodies. tuning fork Fig. 11.3: The production of sound Sound Requires Material Medium for its Propagation waves from a vibrating tuning fork A c t i v i t y 1 1. 2 : U n l i ke l i g h t w a v e s w h i c h a r e Vibrating electromagnetic in nature and can also pass through tuning fork vacuum, sound waves require some material medium for Glass their propagation. This can be proved by bell jar apparatus (Fig. 11.5). The bell jar is placed on the platform of a Water vacuum pump. An electric bell is suspended in the bell jar with the help Fig. 11.4 of two wires connected to a power supply. By setting ON Power supply the power supply, electric bell will begin to ring. We can hear the sound of the bell. Now start pumping out air Bell jar from the jar by means of a vacuum pump. The sound of the bell starts becoming more and more feeble and Electric bell eventually dies out, although bell is still ringing. When Vacuum pump we put the air back into the jar, we can hear the sound of the bell again. From this activity, we conclude that sound waves can only travel/propagate in the presence of air Fig. 11.5: Bell jar apparatus (medium). AOB Longitudinal Nature of Sound Waves (a) OB Propagation of sound waves produced by vibrating tuning fork can be understood by a vibrating tuning fork as shown in Fig.11.6. Before the vibration of tuning fork, density of (b) AO air molecules on the right side is uniform (Fig.11.6-a). When the right prong of tuning fork moves from mean (c) position O to B (Fig.11.6-b), it exerts some pressure on the adjacent layer of air molecules and produces a Fig.11.6: Vibrations of tuning fork compression. after striking with a rubber 21 Not For Sale – PESRP SOUND This compressed air layer in turn compresses the layer Physics Insight next to it and so on. A moment later, the prong begins to move from B towards A (Fig.11.6-c). Now the pressure in the adjacent layer decreases and a rarefaction is produced. This rarefaction is transfered to the air layer next to it and so on. As the tuning fork moves back and forth rapidly, a series of compressions and rarefactions are created in the air. In this way, sound wave propagates Illustration of longitudinal through the air. wave formed by vibrating t u n i n g fo r k i n t h e a i r. As in the Fig.11.6, the direction of propagation of sound wave Compressions are places where air pressure is slightly is along the direction of oscillating air molecules. This shows higher than the surrounding the longitudinal nature of sound waves. Distance between air pressure due to high two consecutive compressions or rarefactions is the density of air particles. While wavelength of sound wave. rarefactions are the regions correspond to low air pressure due to low density of air 11.2 CHARACTERISTICS OF SOUND particles. Sounds of different objects can be distinguished on the basis Quick Quiz of different characteristics as described below: Identify which part of these musical instruments vibrates Loudness: Loudness is the characteristic of sound by which to produce sound: (a) electric bell (b) loud loud and faint sounds can be distinguished. speaker (c) piano (d) violin (e) flute. When we talk to our friends, our voice is low, but when we Self Assessment address a public gathering our voice is loud. Loudness of a 1. Explain how sound is sound depends upon a number of factors. Some of them are produced by a school bell. 2. Why are sound waves called discussed below: mechanical waves? 3.Suppose you and your friend (a) Amplitude of the vibrating body: The loudness of the are on the Moon. Will you be sound varies directly with the amplitude of the able to hear any sound vibrating body (Fig.11.7). The sound produced by a produced by your friend? sitar will be loud if we pluck its wires more violently. Loud Similarly, when we beat a drum forcefully, the Large amplitude of its membrane increases and we hear a amplitude loud sound. Small Quiet amplitude (b) Area of the vibrating body: The loudness of sound Fig. 11.7: Variation of loudness also depends upon the area of the vibrating body. with amplitude Not For Sale – PESRP 22 SOUND For example, sound produced by a large drum is For your information louder than that by small one because of its large Thin-walled glass goblets can vibrating area. If we strike a tuning fork on a rubber vibrate when hit by sound pad, a feeble sound will be heard. But if the vibrating waves. This is due to a phenomenon of sound known tuning fork is placed vertically on the surface of a as resonance. Some singers bench, we will hear a louder sound. From this, we can can produce a loud note of conclude that the loudness increases with the area of particular frequency such that the vibrating body and vice versa. it vibrates the glass so much that it shatters. (c) Distance from the vibrating body: Loudness of sound Interesting information also depends upon the distance of the vibrating body Some people use silent whistle from the listener. It is caused by the decrease in to call dogs whose frequency lies between 20,000 Hz to amplitude due to increase in distance. 25,000 Hz. It is silent for Loudness also depends upon the physical condition of human but not for dogs the ears of the listener. A sound appears louder to a because the audible frequency person with sensitive ears than to a person with range for dogs is much higher. defective ears. However, there is a characteristic of Low pitch sound which does not depend upon the sensitivity of Low the ear of the listener and it is called intensity of sound. frequency Pitch: Pitch is the characteristic of sound by which we can High frequency distinguish between a shrill and a grave sound. High pitch Fig 11.8: Variation of pitch with It depends upon the frequency. A higher pitch means a higher frequency frequency and vice versa. The frequency of the voice of ladies and children is higher than that of men. Therefore, the voice of For your information ladies and children is shrill and of high pitch. The relationship Tuning fork (a) between frequency and pitch is illustrated in Fig. 11.8. Flute Quality: The characteristic of sound by which we can (b) distinguish between two sounds of same loudness and pitch is called quality. Clarinet (c) While standing outside a room, we can distinguish between the notes of a piano and a flute being played inside the room. Fig 11.9: Sound waveforms This is due to the difference in the quality of these notes. produced by (a) a tuning fork, (b) a flute, and (c) a clarinet, are all at approximately the Figure 11.9 shows the waveform of the sound produced by a same frequency. Pressure is tuning fork, flute and clarinet. The loudness and the pitch of p l o tte d ve r t i c a l l y, t i m e 23 Not For Sale – PESRP SOUND these three sounds are the same but their waveforms are different. So their quality is different and they can be distinguished from each other. Quick Quiz 1. Why the voice of women is Intensity more shrill than that of men? 2. Which property of sound The sound waves transfer energy from the sounding body to wave determines its: the listener. The intensity of sound depends on the amplitude (a) loudness (b) pitch? of sound wave and is defined as: 3. What would happen to the loudness of sound with Sound energy passing per second through a unit area held increase in its frequency? perpendicular to the direction of propagation of sound waves is called intensity of sound. Intensity is a physical quantity and can be measured accurately. The unit of intensity of sound is watt per square Do you know? -2 metre (W m ). Frequency of tuning fork depends on the mass of its prongs. The greater the mass, Sound Intensity Level the lower the frequency of The human ear responds to the intensities ranging from vibration which means the -12 -2 -2 10 W m to more than 1 W m (which is loud enough to be lower the pitch. painful). Because the range is so wide, intensities are scaled by factors of ten. The barely audible and the faintest intensity -12 -2 of sound i.e., 10 W m is taken as reference intensity, called zero bel (a unit named after Alexander Graham Bell). The loudness of a sound depends not only on the intensity of sound but also on the physical conditions of the ear. The human ear is more sensitive to some frequencies rather than For your information the others. A sound wave with a frequency The loudness (L) of a sound is directly proportional to the of 3500 Hz and an intensity of logarithm of intensity i.e., 80 dB sounds about twice as L log I loud to us as a sound of 125 Hz L = K log I.......... (11.1) and 80 dB. It is because our ears are more sensitive to the where K is a constant of proportionality. 3500 Hz sound than to the Let Lo be the loudness of the faintest audible sound of intensity 125 Hz. Therefore intensity by Io and L be the loudness of an unknown sound of intensity I, itself does not mean loudness. then by Eq. (11.1), we can write Loudness is how our ears Lo = K log Io.......... (11.2) detect and our brain perceives the intensity of sound waves. Subtracting Eq. (11.2) from Eq. (11.1), we get Not For Sale – PESRP 24 SOUND L - Lo = K (log I - log Io) = K log Table 11.1 I Sources of Intensity Intensity Io Sound -2 (Wm ) level (dB) This difference,(L- Lo), between the loudness L of an unknown sound and the loudness Lois called the intensity level of the 3 unknown sound. Therefore, the intensity level of an Nearby jet 10 150 airplane unknown sound is given by Jackhamm- 1 er/Fast train 10 130 Intensity level = K log.......... (11.3) I 0 Siren 10 120 Io Lawn 100 The value of K depends not only on the units of I and Io but mover 10 -2 also on the unit of intensity level. If intensity I of any Vacuum -5 70 unknown sound is 10 times greater than the intensity Io of cleaner 10 the faintest audible sound i.e., I =10Io and the intensity level Mosquito -8 buzzing 10 40 of such a sound is taken as unit, called bel, the value of K becomes 1. Therefore, using K =1, Eq. (11.3) becomes Whisper -9 30 10 Rustling of -11 10 Intensity level = log (bel).......... (11.4) leaves 10 I Faintest -12 0 Io audible 10 bel is a very large unit of intensity level of a sound. Generally, sound i.e., a smaller unit called decibel is used. Decibel is abbreviated as Threshold (dB). It must be remembered that 1 bel is equal to 10 dB. If the For your information intensity level is measured in decibels, Eq. (11.4) becomes Logarithmic Linear scale scale Intensity level = 10 log (dB).......... (11.5) I Decibels Amplitude Io (dB) (m) Using Eq. (11.5), we can construct a scale for measuring the 0 1 intensity level of sound. Such scale is known as “decibel 20 10 scale”. The intensity level of different sounds in decibel is 40 100 given in Table 11.1. 60 1,000 80 10,000 Example 11.1: Calculate the intensity levels of the (a) faintest audible sound (b) rustling of leaves. 100 1000,000 Solution: (a) Intensity level of faintest audible sound can be 120 1,000,000 -12 -2 calculated by substituting I = Io =10 Wm in Eq. (11.5). The decibel scale is a Therefore, logarithmic measure of the amplitude of sound waves. In a logarithmic scale, equal Intensity level of faintest audible sound = 10 log -12 dB inter vals co rres p o n d to = 0 dB 10-12 multiplying by 10 instead of (b) As the intensity of the rustle of leaves is I 10 -11 -2 =10 W m , adding equal amounts. 25 Not For Sale – PESRP SOUND therefore, -11 -12 Intensity level due to rustling of leaves = 10 log10 /10 dB = 10 log10 dB = 10 dB 11.3 REFLECTION (ECHO) OF SOUND When we clap or shout near a reflecting surface such as a tall Interesting information building or a mountain, we hear the same sound again a little A blue whale's 180 dB rumble is later. What causes this? This sound which we hear is called the loudest animal sound ever an echo and is a result of reflection of sound from the surface. recorded. Whale sounds also appear to be a part of a highly evolved communication system. Some whales are thought to When sound is incident on the surface of a medium it communicate over hundreds and bounces back into the first medium. This phenomenon is may be thousands of kilometres. called echo or reflection of sound. This is possible, in part, because sound waves travel five times faster in water than in air. In The sensation of sound persists in our brain for about 0.1 s. addition, the temperature To hear a clear echo, the time interval between our sound characteristics of ocean water — and the reflected sound must be at least 0.1 s. If we consider decrease in temperature with speed of sound to be 340 ms-1 at a normal temperature in air, depth — create a unique sound phenomenon. we will hear the echo after 0.1 s. The total distance covered by the sound from the point of generation to the reflecting surface and back should be at least 340 m s-1 × 0.1 s = 34.0 m. Thus, for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be half of this distance, i.e., 17 m. Echoes may be heard more than once due to successive or multiple reflections. Do you know? Elephants use low frequency Activity 11.3: Take two identical plastic pipes of suitable sound waves to communicate length, as shown in Fig. 11.10. (We can make the pipes using with one another. Their large chart paper). ears enable them to detect these low frequency sound  Arrange the pipes on a table near a wall. waves, which have relatively  Place a clock near the open end of one of the pipes and long wavelengths. Elephants try to hear the sound of the clock through the other pipe. can effectively communicate in  Adjust the position of the pipes so that you can hear this way, even when they are the sound of the clock clearly. separated by many kilometres.  Now, measure the angles of incidence and reflection and see the relationship between the angles. Not For Sale – PESRP 26 SOUND  Lift the pipe on the right vertically to a small height and observe what happens. Screen For your information Angle of Angle of reflection Wall incidence Wave on screen Microphone Pipe Table Clock i r Ear Amplifier Oscilloscope By using an oscilloscope, you can “see” sound waves. Fig. 11.10: Reflection of sound 11.4 SPEED OF SOUND Table 11.1 Speed of sound in various Sound waves can be transmitted by any medium containing media particles that can vibrate. They cannot pass through vacuum. Medium Speed (m s-1) Gases However, the nature of the medium will affect the speed of Air(0oC) 331 the sound waves. In general, the speed of sound in a liquid is 0 Air (25 C) 346 five times that in gases; the speed of sound in solid is about Air(100oC) 386 fifteen times that in gases. The speed of sound in air is Hydrogen (0oC) 1290 affected by changes in some physical conditions such as Oxygen (0oC) 317 Helium (0oC) 972 temperature, pressure and humidity etc. Liquids at 250C The speed of sound in air is 343 m s-1 at one atmosphere of Distilled water 1498 pressure and room temperature (21°C). The speed varies Sea water 1531 with temperature and humidity. The speed of sound in solids Solids 250C and liquids is faster than in air. Following relation can be used Wood 2000 Aluminium 6420 to find the speed of sound: Brass 4700 v = f λ........ (11.6) Nickel 6040 Iron 5950 where v is the speed, f is the frequency and λ is the Steel 5960 wavelength of sound wave. Flint Glass 3980 Example 11.2: Calculate the frequency of a sound wave of -1 speed 340 m s and wavelength 0.5 m. -1 Solution: Given that; speed of waves v = 340 m s 27 Not For Sale – PESRP SOUND Wavelength λ = 0.5 m Using the formula v = f λ Putting the values -1 f = 340 m s /0.5 m = 680 Hz Measuring Speed of Sound by Echo Method Do you know? Apparatus: Measuring tape, stopwatch, flat wall that can produce a good echo. B Procedure: A 1. Use the tape to measure a distance of 50 metres from the wall. 2. Now clap your hands in front of the wall at a distance The speed of sound in air was of 50 metres and check if you can clearly hear first accurately measured in an echo from the wall. Make sure the echo is not 1738 by members of the French coming from any other wall in the area. The time taken by Academy. Two cannons were set up on two hills the sound to travel 100 metres is the time approximately 29 km apart. By difference between the clap and the echo. measuring the time interval 3. Now restart the clapping and start the stopwatch at between the flash of a cannon and the “boom”, the speed of the first clap. Count the number of claps, and sound was calculated. Two stop the clapping and the stopwatch when you hear cannons were fired the echo of the 10th clap (say). alternatively to minimize errors due to the wind and to delayed 4. Now find the average time for 10 claps. After reactions in the observers. calculating the time interval t between claps From their observations, they and using the formula S = vt, we can calculate the deduced that sound travels at -1 speed of the sound. about 336 m s at 00C. Example 11.3: Flash of lightning is seen 1.5 seconds earlier than the thunder. How far away is the cloud in which the flash has occurred? (speed of sound = 332 m s-1). Solution: Given that, time t = 1.5 s, speed of sound v = 332 m s-1. Therefore, distance of the cloud S = vt = 1.5 s × 332 m s-1= 498 m. 11.5 NOISE POLLUTION We enjoy the programmes on radio or television by hearing sounds of different qualities. In musical programmes, we hear sound produced by musical instruments such as flute, harmonium, violin, drum etc. Sound of these instruments has pleasant effect on our ears. Such sounds which are pleasant to Not For Sale – PESRP 28 SOUND our ears are called musical sounds. However, some sounds produce unpleasant effects on our ears such as sound of machinery, the slamming of a door, and sounds of traffic in big Physics insight cities. Sound which has jarring and unpleasant effect on our ears is called noise. Noise corresponds to irregular and sudden vibrations produced by some sounds. Noise pollution has become a major issue of concern in big cities. Noise is an undesirable sound that is harmful for health of human and other species. Transportation equipment and heavy machinery are the main sources of noise pollution. For Reflection example, noise of machinery in industrial areas, loud vehicle horns, hooters and alarms. Noise has negative effects on human health as it can cause conditions such as hearing loss, sleep disturbances, aggression, hypertension, high stress levels. Noise can also cause accidents by interfering with communication and warning signals. A safe level of noise depends on two factors: the level Refraction (volume) of the noise; and the period of exposure to the noise. The level of noise recommended in most countries is usually 85-90 dB over an eight-hour workday. Noise pollution can be reduced to acceptable level by replacing the noisy machinery with environment friendly machinery and equipments, putting sound-reducing barriers, or using hearing protection devices. Diffraction Activity 11.4: Develop an action plan to help you address any problem(s) with noise in your workplace considering the following points: 1. Describe the problem(s). 2. What are the sources of the problem(s)? 3. Who are the people being affected? 4. Your suggestions for the solution. Absorption Sound displays all the 11.6 IMPORTANCE OF ACOUSTICS properties of waves when it interacts with materials and The technique or method used to absorb undesirable sounds boundaries. by soft and porous surfaces is called acoustic protection. Reflection of sound is more prominent if the surface is rigid and smooth, and less if the surface is soft and irregular. Soft, 29 Not For Sale – PESRP SOUND porous materials, such as draperies and rugs absorb large For your information amount of sound energy and thus quiet echoes and softening Bat noises. Thus by using such material in noisy places we can Prey reduce the level of noise pollution. However, if the surface of classrooms or public halls are too absorbent, the sound level may be low for the audience. Sometimes, when sound reflects from the walls, ceiling, and floor of a room, the The phrase “blind as a bat” is a reflecting surfaces are too reflective and the sound becomes false statement. Bats have some garbled. This is due to multiple reflections called vision using light, but when reverberations. In the design of lecture halls, auditorium, or placed in pitch-black rooms theater halls, a balance must be achieved between crisscrossed with fine wires, they reverberation and absorption. It is often advantageous to can easily fly around and unerringly locate tiny flying place reflective surfaces behind the stage to direct sound to insects for food. We usually the audience. assume that vision requires light but both bats and dolphins have Generally, the ceilings of lecture halls, conference halls and the ability to “see” using sound theatre halls are curved so that sound after reflection may waves. Research in science and technology has developed reach all the corners of the hall (Fig 11.11). Sometimes “eyes” that enable humans also curved sound boards are placed behind the stage so that to see using sound waves. sound after reflection distributed evenly across the hall (Fig. 11.12). Soundboard For your information Source of sound Fig. 11.11: Curved ceiling of a conference hall Fig. 11.12: Soundboard used in a big hall 11.7 AUDIBLE FREQUENCY RANGE We know that sound is produced by a vibrating body. A Pilots wear special normal human ear can hear a sound only if its frequency lies headphones that reduce the between 20Hz and 20,000 Hz. In other words, a human ear roar of an airplane engine to a neither hears a sound of frequency less than 20 Hz nor a quiet hum. sound of frequency more than 20,000 Hz. Different people have different range of audibility. It also decreases with age. Young children can hear sounds of 20, 000 Hz but old people cannot hear sounds even above 15, 000 Hz. Not For Sale – PESRP 30 SOUND Tidbits The range of the frequencies which a human ear can hear is Bats can hear frequencies up called the audible frequency range. to 120,000 Hz. Other animals cannot hear such high-pitched 11.8 ULTRASOUND s o u n d s. M i c e ca n h e a r frequencies up to 100,000 Hz, Sounds of frequency higher than 20, 000 Hz which are dogs up to 35,000 Hz, and cats inaudible to normal human ear are called ultrasound or up to 25,000 Hz. Humans hear ultrasonics. sounds only upto about 20,000 Hz, but children can usually hear Uses of Ultrasound higher-frequency sounds than adults.  Ultrasonic waves carry more energy and higher frequency than audible sound waves. Therefore, according to the wave equation v = f λ, the wavelength of ultrasonic waves is very small and is very useful for detecting very small objects.  Ultrasonics are utilized in medical and technical fields.  In medical field, ultrasonic waves are used to diagnose and treat different ailments. For diagnosis of different diseases, ultrasonic waves are made to enter the human body through transmitters. These waves are reflected differently Fig. 11.13: Doctors are taking by different organs, tissues or tumors etc. The ultrasound test of a patient reflected waves are then amplified to form an with an ultrasound machine image of the internal organs of the body on the screen (Fig.11.13). Such an image h e l p s i n detecting the defects in these organs.  Powerful ultrasound is now being used to remove blood clots formed in the arteries.  Ultrasound can also be used to get the pictures of Boat thyroid gland for diagnosis purposes. (or ship)  Ultrasound is used to locate underwater depths or is Water used for locating objects lying deep on the surface Detector ocean floor, etc. The technique is called SONAR, Transmitter (sound navigation and ranging). The sound waves are Seabed sent from a transmitter, and a receiver collects the reflected sound (Fig.11.14). The time-lapse is Fig. 11.14: Ultrasonics are calculated, knowing the speed of used to measure the depth of sound in water, the distance of the object from the water by echo method ocean surface can be estimated. 31 Not For Sale – PESRP SOUND  SONAR ranging is also used to see the shape and the size of the object. Cracks appear in the interior of moving parts of high speed heavy machines such as turbines, engines of ships and airplanes due to excessive use. These cracks are not visible from outside but they can be very dangerous. Such cracks can be detected by ultrasonics. A powerful beam of ultrasound is made to pass through these defective parts. While passing, these waves are reflected by the surface of these cracks and flaws. The comparison of the ultrasonic waves reflected from cracks and from the surfaces of these parts can give a clue of the existence of the cracks.  Germs and bacteria in liquids can also be destroyed by using high intensity ultrasonic waves. SUMMARY   Sound is produced by a vibrating body. It travels in the medium from one place to another in the form of compressional waves. Loudness is a feature of sound by which a loud and a faint sound can be distinguished. It depends upon the amplitude, surface area and distance from the vibrating body.   Sound energy flowing per second through unit area held perpendicular to the direction of sound waves is called the intensity of sound. bel is unit of the intensity level of sound, where 1 bel = 10 decibels  Pitch of the sound is the characteristics of sound by which a shrill sound can be distinguished from a grave one. It depends upon the frequency. The characteristics of sound by which two sound waves of same loudness and pitch are distinguished from each other is called the quality of sound.   The sounds with jarring effect on our ears are called noise and the sounds having pleasant effect on our ears are called musical sounds. Noise pollution has become a major issue of concern in some big cities. Any form of sound which disturbs the normal functioning of any natural ecosystem or some human community is the cause of noise pollution.  Noise pollution can be reduced to acceptable level by replacing the rusty noisy machinery with environment friendly machinery and equipments, putting sound- reducing barriers, or using hearing protection devices.  The technique or method used to absorb undesirable sound energy by soft and porous surfaces is called acoustic protection. This can be done by using soft, rough and porous materials. Not For Sale – PESRP 32 SOUND  Human audible frequency range lies between 20 Hz to 20, 000 Hz.  Sound waves of frequency higher than 20, 000 Hz are called ultrasound while sound waves of frequency lower than 20 Hz are called infrasound.  Ultrasound is used in many fields of science and technology such as medical, engineering, agriculture. In medical field ultrasound is used to diagnose and treat different ailments. Ultrasound is also used to locate underwater depths or for locating objects lying deep on the ocean floor. The technique is called SONAR, an acronym for sound navigation and ranging. MULTIPLE CHOICE QUESTIONS Choose the correct answer from the following choices: i. Which is an example of a longitudinal wave? (a) sound wave (b) light wave (c) radiowave (d) water wave ii. How does sound travel from its source to your ear? (a) by changes in air pressure (b) by vibrations in wires or strings (c) by electromagnetic wave (d) by infrared waves iii. Which form of energy is sound? (a) electrical (b) mechanical (c) thermal (d) chemical iv. Astronauts in space need to communicate with each other by radio links because (a) sound waves travel very slowly in space (b) sound waves travel very fast in space (c) sound waves cannot travel in space (d) sound waves have low frequency in space v. The loudness of a sound is most closely related to its (a) frequency (b) period (c) wavelength (d) amplitude vi. For a normal person, audible frequency range for sound wave lies between (a) 10 Hz and 10 kHz (b) 20 Hz and 20 kHz (c) 25 Hz and 25 kHz (d) 30 Hz and 30 kHz vii. When the frequency of a sound wave is increased, which of the following will decrease? i. wavelength ii. period iii. amplitude (a) i only (b) iii only (c) i and ii only (d)