Waves and Sound 1 Lecture Notes PDF

Waves and Sound 1 The Nature of Waves  A wave is a traveling disturbance and carries energy from place to place.  Waves can be classified into two main categories, transverse and longitudinal waves Transverse Wave  In a transverse wave, the disturbance occurs perpendicular to the directio...

Waves and Sound 1 The Nature of Waves  A wave is a traveling disturbance and carries energy from place to place.  Waves can be classified into two main categories, transverse and longitudinal waves Transverse Wave  In a transverse wave, the disturbance occurs perpendicular to the direction of travel of the wave. Longitudinal wave  In a longitudinal wave, the disturbance occurs parallel to the line along which the wave travels. Periodic Wave  A periodic wave consists of cycles or patterns that are produced over and over again Parameters Concerning Waves  The amplitude of the wave is the maximum excursion of a particle of the medium from the particle’s undisturbed position.  The wavelength  is the distance along the length of the wave between two successive equivalent points, such as two crests or two troughs.  The period T is the time required for the wave to travel a distance of one wavelength.  The frequency f (in hertz) is the number of wave cycles per second that passes an observer and is the reciprocal of the period (in seconds):  The speed v of a wave is related to its wavelength and frequency according to  Example  AM and FM radio waves are transverse waves consisting of electric and magnetic disturbances traveling at a speed of 3  108 m/s. A station broadcasts an AM radio wave whose frequency is 1230  103 Hz (1230 kHz on the dial) and an FM radio wave whose frequency is 91.9  106 Hz (91.9 MHz on the dial). Find the distance between adjacent crests in each wave. Solution  The distance between adjacent crests is the wavelength (). Since the speed of each wave is v = 3  108 m/s and the frequencies are known, the relation v = f can be used to determine the wavelength   The Mathematical Description of Waves  When a wave of amplitude A, frequency f, and wavelength  moves in the +x direction through a medium, the wave causes a displacement y of a particle at position x according to   For a wave moving in the -x direction, the expression is  The wave equation shows the displacement y of this particle from its undisturbed position at any time t as the wave passes. Example A transverse periodic wave described by the expression (where y and x are in meters and t is in seconds) is established on a string. Which one of the following statements concerning this wave is false? (a) The wave is traveling in the negative x direction. (b) The amplitude is 1.0 m. (c) The frequency of the wave is 0.10 Hz. (d) The wavelength of this wave is 2.0 m. (e) The wave travels with speed 5.0 m/s. Example A wave has an amplitude of 0.35 m, a frequency of 1.05 × 106 Hz, and travels in the positive x direction at the speed of light, 3.00 × 108 m/s. Which one of the following equations correctly represents this wave? (a) y = 0.35 sin (6.60 × 106t − 0.022x) (b) y = 0.35 sin (286t + 1.05 × 106x) (c) y = 0.35 sin (6.60 × 106t + 0.022x) (d) y = 0.35 sin (1.05 × 106t + 3.00 × 108x) (e) y = 0.35 sin (286t − 1.05 × 106x) Check Your Understanding A loudspeaker produces a sound wave (a periodic longitudinal wave) that travels from air into water. The wave frequency does not change, because the loudspeaker producing the sound determines the frequency. The speed of sound in air is 343 m/s, whereas the speed in fresh water is 1482 m/s. When the sound wave enters the water, does its wavelength a) increase b) decrease, or c) remain the same? The Nature of Sound  Sound is a longitudinal wave that is created by a vibrating object, such as a guitar string, the human vocal cords  Sound can be created or transmitted only in a medium, such as a gas, liquid, or solid.(Mechanical Waves)  Each cycle of a sound wave includes one condensation (a region of greater than normal pressure) and one rarefaction (a region of less than normal pressure).  A sound wave with a single frequency is called a pure tone.  Experiment have shown that a healthy young person hears all sound frequencies from approximately 20 to 20 000 Hz (20 kHz)  Frequencies less than 20 Hz are called infrasonic.  Frequencies greater than 20 kHz are called ultrasonic  The brain interprets the frequency detected by the ear primarily in terms of the subjective quality known as pitch.  A high-pitched sound is one with a large frequency (e.g., piccolo). A low-pitched sound is one with a small frequency (e.g., tuba).  The pressure amplitude of a sound wave is the magnitude of the maximum change in pressure, measured relative to the undisturbed pressure.  The pressure amplitude is associated with the subjective quality of loudness.  The larger the pressure amplitude, the louder the sound. Piccolo Tuba The Speed of Sound  The speed of the sound wave v depends on the material that propagates the sound  In air at 20 C, the speed of sound is about 330 m/s, and in water it is about 1400 m/s  The pressure variations due to the propagating sound are superimposed on the ambient air pressure Sound Intensity  The sound intensity I is defined as the sound power P that passes perpendicularly through a surface divided by the area A of that surface:  The SI unit for intensity is watts per square meter (W/m2) Example  In Figure shown 1210-5 W of sound power passes perpendicularly through the surfaces labeled 1 and 2. These surfaces have areas of A1 = 4 m2 and A2 = 12 m2. Determine the sound intensity at each surface and discuss why listener 2 hears a quieter sound than listener 1. Solution  The sound intensity at each surface follows from the intensity equation Surface 1 Surface 2  When a source radiates sound uniformly in all directions and no reflections are present, the intensity of the sound is inversely proportional to the square of the distance from the source, according to Example  During a fireworks display, a rocket explodes high in the air above the observers. Assume that the sound spreads out uniformly in all directions and that reflection from the ground can be ignored. When the sound reaches listener 2 in Figure, who is r2 = 640 m away from the explosion, the sound has an intensity of I2 = 0.10 W/m2. What is the sound intensity detected by listener 1, who is r1 = 160 m away from the explosion? Solution The ratio of the sound intensities can be found using last equation for power: As a result  The ear responds to an enormous range of intensities  At 3000 Hz, the lowest intensity that the human ear can detect is about 10-12 W/m2 (Threshold of hearing)  The loudest tolerable sound has an intensity of about 10 -4 W/m2 (Threshold of pain)  Sound intensities above the threshold of pain may cause permanent damage to the eardrum Check Your Understanding  Some animals rely on an acute sense of hearing for survival, and the visible parts of the ears of such animals are often relatively large. How does this anatomical feature help to increase the sensitivity of the animal’s hearing to low- intensity sounds?  A source is emitting sound uniformly in all directions. There are no reflections anywhere. A flat surface faces the source. Is the sound intensity the same at all points on the surface? Problems 1. A wave traveling along the x axis is described mathematically by the equation where y is the displacement (in meters), t is in seconds, and x is in meters. What is (a) the frequency, (b) the wavelength, and (c) the speed of the wave? 2. A wave traveling in the +x direction has an amplitude of 0.35 m, a speed of 5.2 m/s, and a frequency of 14 Hz. Write the equation of the wave? 3. The average sound intensity inside a busy neighborhood restaurant is 3.2  10-5 W/m2. How much energy goes into each ear (area = 2.1  10-3 m2) during a one-hour meal? 4. At a distance of 3.8 m from a siren, the sound intensity is 3.6  10-2 W/m2. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated.