Sound Waves PDF - European University Cyprus

Sound Waves Irene Polycarpou What is a wave? A WAVE is a vibration or disturbance in space. A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move. Types of waves A wave is a form of energy transfer. MECHANICAL ELECTROMAGNETI...

Sound Waves Irene Polycarpou What is a wave? A WAVE is a vibration or disturbance in space. A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move. Types of waves A wave is a form of energy transfer. MECHANICAL ELECTROMAGNETIC Needs a medium to propagate. Does not need a medium to propagate. i. Water ii. Sound i. X-rays ii. Radio waves iii. Light Direction of propagation Depending on the direciton of propagation, waves can further be categorized into: a. Transverse b. Longitudinal Direction of propagation TRANSVERSE WAVE The particles of the medium oscillate (vibrate) perpendicular to the motion of the wave. ❑E.g. water wave, electromagnetic waves travelling in a medium LONGITUDINAL WAVE The particles of the medium oscillate parallel to the motion of the wave. A longitudinal wave has two main sections: 1. Compression – an area of high molecular density and pressure 2. Rarefaction – an area of low molecular density and pressure  Particles of the medium oscillate parallel to the motion of the wave. COMPRESSION RAREFACTION Particles of the medium oscillate perpendicular to the motion of the wave. Each wave can be described by… ✓ The wavelength, 𝜆, is the distance between two successive maxima (“peaks”) or minima (“troughs”) in the wave. [m] ✓ The amplitude, 𝐴, is the maximal distance that a particle in the medium is displaced from its equilibrium position. [dB] ✓ The velocity, 𝑣⃗ , is the velocity with which the disturbance propagates through the medium. [m/s] ✓ The period, 𝑇, is the time it takes for two successive maxima (or minima) to pass through the same point in the medium. ✓ The frequency, 𝑓, is the inverse of the period (𝑓=1/𝑇). [Hz] Wave speed You can find the speed of a wave by multiplying the wave’s wavelength in meters by the frequency (cycles per second). Since a “cycle” is not a standard unit this gives you meters/second. Example A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s. What is the wavelength? cycles 40 f = = = 1.33 Hz sec 30 x 4.25 v= = = 0.425 m/s t 10 vwave vwave = f →  = = 0.319 m f Sound waves Longitudinal mechanical waves that propagate through a medium. Sound is a sensation created in the human brain in response to pressure fluctuations in the air. As any object moves through the air, the air near the object is disturbed. The disturbances are transmitted through the air at the speed of sound. 1. Air pressure waves. 2. Tympanic membrane vibrates → transforms vibration into mechanical energy 3. Middle ear converts energy into hydraulic energy in the fluid of the inner ear. 4. Hydraulic energy stimulates the sensory cells of the inner ear, which send electrical impulses to the auditory nerve, brainstem, and cortex. Energy Conversion 1. Sound energy 2. Mechanical energy 3. Hydraulic energy 4. Chemical energy 5. Electrical energy Sound waves Sound is a longitudinal wave. Sound waves Sound is a longitudinal wave. ✓ Needs a medium to propagate. ✓ Particles move in a direction paralell to the direction of wave propagation. Sound waves Sound is a longitudinal wave. As the bell moves back and forth, the edge of the bell strikes particles in the air. 1. Bell moves forward → 2. Bell moves backward → particles driven forward particles driven backward i. Air particles bounce with i. Air particles bounce with Pressure variations greater velocity lower velocity transmitted through ii. Greater pressure ii. Lower pressure matter as sound waves. Sound waves Sound: mechanical disturbance generated by passage of energy through a medium. ✓ Source generates and propagates mechanical vibrations between the particles of the medium → sound wave Sound waves Imagine a material as an array of molecules linked by springs As an ultrasound pressure wave propagates through the medium, molecules in regions of high pressure will be pushed together (compression), whereas molecules in regions of low pressure will be pulled apart (rarefaction). As the sound waves propagate through a medium, molecules oscillate around equilibrium position. Propagation of sound waves Sound is characterized by the properties of sound waves (i.e. frequency, wavelength, speed, period, amplitude) Sound waves can propagate in solids, liquids and gases. Sound propagate as waves of alternating pressure, causing local regions of compression and rarefaction. The particles of the material transmitting this wave oscillate in the direction of propagation of the wave itself. Sound waves that are confined to the frequency range which can stimulate the human ear and brain, lead to the sensation of hearing. Sound vs. light SOUND LIGHT Mechanical wave Electromagnetic wave Longitudinal wave Transmit Transverse wave Amplitude tells you energy Amplitude tells you about about volume Do NOT intensity Frequency tells you transmit matter Frequency tells you about about pitch type of wave / color Speed in air 346 m/s Can reflect, Speed of light in air 3 x 108 Sound travels faster in diffract, interfere m/s and diffract most solids than it does Light slows down in solids in air Measured in Travels through vacuum The denser the medium, Herz (Hz) The denser the medium, the faster the wave the slower the wave Measured in decibels (dB) Perception of sound Sound is perceived through the sense of hearing. Hearing is one of the senses and refers to the ability to detect sound. Sound is detected by the ear and transduced into nerve impulses that are perceived by the brain. Frequency range of sound waves The human ear does not respond uniformly to sounds at all frequencies. Human can hear sounds with frequencies between 20Hz and 20kHz. Power and intensity of a sound wave Travelling sound waves transport energy from one point to another. A sound wave transports energy through a medium from a source. The energy is measured in Joules [J] Power (P) – rate at which the source produces energy. Measured in Watts [W], where 1 W = 1 J/s Intensity (I) – power per unit area. Measured in [W/m2 = dB] Power and intensity associated with a wave increase with pressure [p]. P∝p I∝p 2 Intensity is a measure of the amount of energy in sound waves. Intensity of a sound wave Pressures in two sound waves of different intensities. The more intense sound is produced by a source that has larger amplitude oscillations and has greater pressure maxima and minima. Higher pressure associated with more intense sounds → exerts larger forces on the objects it encounters. The loudness of a sound is determined by the intensity of the sound waves. Pitch of a sound wave The sensation of a frequency is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency sound wave. A low pitch sound corresponds to a low frequency sound wave. Pitch of a sound wave Loudness vs. pitch Loudness vs. pitch Wavelengths of sound waves The shorter the wavelength, the higher the frequency, and the higher the pitch, of the sound. In other words, short waves sound high; long waves sound low. Noise-induced hearing loss Noise-induced hearing loss Noise-induced hearing loss (NIHL) occurs when structures in the inner ear become damaged due to loud noises. What part of the ear is damaged in noise-induced hearing loss? Loud noises primarily affect the cochlea, an organ within the inner ear. When you’re exposed to loud noises, cells and membranes in the cochlea can become damaged. Loud sound → stronger vibration → damage to cells & membranes in the Cochlea decibels [dB] Higher intensity = higher amplitude Energy and Power Speed (c) at which a sound wave travels is determined by the medium. Units are meters per second [m/s]. The material properties which determine speed of sound are density (𝜌) [mass per unit volume] and elasticity (k), or stiffness. Wave speed Sound waves are longitudinal waves (i.e. involve oscillations parallel to the direction of wave travel) that propagate through a medium (e.g. air, water, iron). Speed of sound: the speed of any mechanical wave devepends on both the inertial property of the medium (stores kinetic energy) and the elastic (stores potential energy) Stretched string – the speed of the “transverse” wave along a stretched string Sound – the speed of the “longitudinal” sound wave is Complex sounds You can add up single You can take a complex sound frequencies to make a complex and break it down into single sound. frequencies. Fourier’s Theorem Fourier’s Theorem – any repetitive wave can be reproduced exactly by combining simple sine waves of different frequencies and amplitudes Example 1 How can this 100 Hz square wave be reproduced from a combination of sine waves? ✓ The first four sine waves in the Fourier series (100 Hz, 300 Hz, 500 Hz, and 700 Hz) add up to a fairly good approximation. ✓ Adding more waves will make the approximation even better Fourier series - expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines  If two waves are at the same place at the same time, they superimpose This means that their amplitudes add together vectorially Principle of superposition – When two or more waves cross at a point, the displacement at that point is equal to the sum of the displacements of the individual waves. Superposition of waves Interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. Superposition of waves Constructive interference – two waves overlap in such a way that they combine to create a larger wave. ✓ occurs when the phase difference between the waves is an even multiple of π (180°) Destructive interference – two waves overlap in such a way that they cancel each other out. ✓ occurs when the difference is an odd multiple of π Interaction of waves with matter The wave doesn't just stop when it reaches the end of the medium. Rather, a wave will undergo certain behaviours when it encounters the end of the medium. At long wavelengths, At medium wavelengths, At low wavelengths, a shadow is sound passes through sound is re-radiated at cast by the obstacle and sound is obstacles. edges of obstacles. reflected back to source. Interaction of waves with matter TRANSMISSION REFLECTION SCATTERING DIFFRACTION REFRACTION Diffraction Involves a change in direction of waves as they pass through an opening or around a barrier in their path. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. We notice sound diffracting around corners or through door openings, allowing us to hear others who are speaking to us from adjacent rooms. Diffracted sound wave has poor sound tone and quality. Reflection When a wave reaches the boundary between mediums, a portion of the wave undergoes reflection, and a portion of the wave undergoes transmission across the boundary. The amount of reflection is dependent upon the dissimilarity of the two media. Reflected sound wave results into difference in frequency making the pitch of the observed sound poor/ echo/ reverberation. Reflection Laws of reflection at plane surface: 1. Incident ray, reflected ray and the normal ray all lie in the same plane. 2. Incident angle is equal to the reflected angle. Refraction When sound changes mediums (enters a different material) at an angle other that 90 degrees, it is bent from its original direction. Because of the angle, part of the wave enters the new medium first and changes speed. The speed of sound in air is affected by the temperature of the medium, the wave moving faster at higher temperatures and slower at cool temperatures. Molecules at higher temperatures have more energy and can vibrate faster and allow sound waves to travel more quickly. Standing vs Travelling wave Standing wave – forms when two waves of equal amplitude and frequency are traveling in opposite directions. Superposition of two travelling waves. Traveling Wave – is a wave that is moving. It may be either longitudinal or transverse, but will move in the direction of propagation. Standing wave A standing (stationary) wave is a combination of two waves moving in opposite direction – each with same amplitude and frequency ❑A standing wave is produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave: 1. Node – Areas of ZERO AMPLITUDE 2. Antinode – Areas of MAXIMUM AMPLITUDE. Standing wave The frequencies of the standing waves on a particular string are called resonant frequencies. They are also referred to as the fundamentals and harmonics. Harmonics – Closed pipe A closed pipe is one where one end is open and the other is closed. Like open pipes, these can form a standing wave with sound of an appropriate frequency. In this case, there can be a standing wave whenever the wavelength allows an antinode at the open end of the pipe and a node at the closed end. Harmonics – Closed pipe Have an antinode at one end and a node at the other. Each sound you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound? You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength. This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC. Harmonics – Closed pipe Harmonics are multiples of the fundamental frequency. In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced. Harmonics – Closed pipe In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced. ✓ CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS! Harmonics – Open pipe The first resonant frequency for an open pipe occurs at ½ of wavelength for a wave. The peaks of the wave will be placed at the ends of the tube. This will create the loudest sound! Harmonics – Open pipe The next resonant frequency occurs at one wavelength. The peaks of the wave still occur at the open ends of the tube. This will create the loudest sound! The third frequency at which resonance occurs is at 1 ¼ wavelength Doppler effect The shift in frequency caused by motion is called the Doppler effect. Doppler effect - change in the frequency of a wave in relation to an observer who is moving relative to the source of the wave. Speed of sound The speed of sound in air is 343 meters per second (660 miles per hour) at one atmosphere of pressure and room temperature (21°C). An object is subsonic when it is moving slower than sound. We use the term supersonic to describe motion at speeds faster than the speed of sound. Mach number The ratio of the speed of the source to the speed of sound determines the presence of shock waves. Because of the importance of this speed ratio, aerodynamicists have designated it with a special parameter called the Mach number in honor of Ernst Mach, a late 19th century physicist who studied gas dynamics. Mach number is the ratio of flow velocity past a boundary to the local speed of sound Breaking of the sound barrier Application of sound Because sound is a wave, it can be reflected and refracted just as light. Reflection common in sound waves. Echo is an example of reflection. Uses of ECHOES: ✓ Used to find the distance between the source and the reflected object by determining the time taken for the echo to return to the source. Example 2 A sound wave moving with a speed of 1500 m/s is sent from a submarine to the ocean floor. It reflects off the ocean floor 5 seconds later. How far is the ocean floor? Application of sound Stethoscope as a collector of sounds. These sounds, such as the heartbeat, originate from the body and are transmitted, through tubes, and the air inside the tube, to the ears of the physician. Stethoscope Consists of three main parts: 1. Chest piece Small disc-shaped resonator (diaphragm) which is very sensitive to sound and amplifies the sound it detects. 2. Ear piece Metal tubes which are used to hear sounds detected by the chest piece. 3. Rubber tube Used to transmit the sound signal detected by the diaphragm to the ear piece. Sound produced by internal organs can be detected, and it reaches the ear piece through this tube by multiple reflections. Stethoscope PARTS Stethoscope HOW DOES IT WORK? Stethoscope APPLICATION Uses of stethoscope: Heart Lungs and Airways Abdomen Percussion  https://news.vin.com/default.aspx?pid=210&catId=617&id=7264532 Acoustic vs electronic stethoscope Sound Quality Acoustic Stethoscope: Uses tubes for direct sound transmission. Electronic Stethoscope: Enhances sound with electronic amplification and filtering. Application of sound Sound waves are also used in imaging machines such as ultrasound. ✓ Allows us to visualize the fetus. ✓ Much healthier than using x-rays (because this might damage the fetus). Ultrasound machine – good example of reflection and refraction of sound waves. Ultrasound Ultrasound – sound waves of high frequency; unaudible to humans Sound waves with a frequency above 20 kHz Ultrasound frequencies used for imaging are 2 - 15 MHz The velocity and the attenuation of the ultrasound wave are dependent on the properties of the medium through which it is travelling. Like normal sound, ultrasound echoes off objects. Examples of ultrasound: ✓ Bats ✓ Dolphins ✓ Submarines (sonar) Ultrasound frequencies for imaging 2.5 MHz: deep abdomen, obstetric and gynaecological imaging 3.5 MHz: general abdomen, obstetric and gynaecological imaging 5.0 MHz: vascular, breast, pelvic imaging 7.5 MHz: breast, thyroid 10.0 MHz: breast, thyroid, superficial veins, superficial masses, musculoskeletal imaging. 15.0 MHz: superficial structures, musculoskeletal imaging. Ultrasound Uses high-frequency sound waves to image the body. It is a real-time investigation which allows assessment of moving structures and facilitates measurement of velocity and directionality of blood flow within a vessel. Basic principles of image formation Doppler ultrasound describes a frequency shift between an emitted ultrasound beam and the received echo. It has three components: 1. Source / transmitter / emitter. 2. Receiver / observer / detector. 3. Physical propagation medium. Basic principles of image formation 1. Ultrasound pulse is launched into the tissue. 2. At tissue interface, a portion of the ultrasound signal is transmitted into the second tissue. 3. A portion is reflected within the first tissue (echo). 4. Echo signal detected by the transducer. Ultrasound interactions INTERACTION OF WAVES WITH THE TISSUE Reflection Scattering Refraction Attenuation and absorbtion Diffraction Ultrasound propagation BASIC ACOUSTICS Reflection: Ultrasound waves bounce back when they encounter tissue interfaces with different acoustic properties. Refraction: Ultrasound waves change direction when they pass through tissues at oblique angles due to variations in sound speed. Attenuation: Ultrasound waves lose intensity as they travel through tissue due to factors like absorption, scattering, and reflection. REFLECTION For a flat, smooth surface, the angle of reflection (r) = the angle of incidence (i) Since the body surfaces are not usually smooth or flat, then 𝑟 ≠ 𝑖 SCATTERING Reflection occurs at large interfaces such as those between organs where there is a change in acoustic impedance. Within most organs, there are many small-scale variations in acoustic properties which constitute small-scale reflecting targets. Reflection from small targets does not follow laws of reflection for large interfaces → scattering Scattering redirects energy in all directions, but is a weak interaction compared to reflection at large interfaces. REFRACTION When an ultrasound wave crosses a tissue boundary at an angle (non-normal incidence), where there is a change in the speed of sound c, the path of the wave is deflected as it crosses the boundary. Snell's law, also known as the Snell-Descartes law, relates the incidence and refraction angles to the refraction indices of the media involved. ATTENUATION As an ultrasound wave propagates through a medium, the intensity reduces with distance travelled. Attenuation ✓ describes the reduction in intensity with distance and includes scattering, diffraction and absorption ✓ decreases linearly with frequency Attenuation limits the frequency that can be used → tradeoff between penetration depth and resolution. ABSORPTION In soft tissues, most energy loss (attenuation) is due to absorption Absorption – process by which ultrasound energy is converted to heat in the medium. Responsible for heating of the tissue Attenuation and absorption are often expressed in terms of decibels. DIFFRACTION Diffraction – process by which the ultrasound wave diverges (spreads out) as it moves away from the source. Divergence is determined by the relationship between the width of the source (aperture) and the wavelength of the wave. Interaction of ultrasound with tissue 1. Emit high-frequency ultrasound waves into the body. 2. Waves encounter tissue interfaces and produce reflections based on differences in density and acoustic impedance. 3. Some waves are absorbed by the tissue as they pass through; denser tissues absorb more energy. 4. The remaining waves transmit through the tissue. 5. Analyze returning echoes. Interaction of ultrasound with tissue Ultrasound acts like a bat. Emits ultrasound and detects echoes → maps out boundaries of objects. If a source of sound moves towards the listener, the waves begin to catch up with each other. The wavelength gets shorter and so the frequency gets higher – the sound has a higher pitch. We use this principle to work out how fast blood cells move. Ultrasound reflects off the blood cells and causes a Doppler shift. STATIONARY BLOOD CELL The ultrasound probe emits an ultrasound wave. A stationary blood cell reflects the incoming wave with the same wavelength → there is no Doppler shift. MOVING BLOOD CELL The ultrasound probe emits an ultrasound wave. A blood cell moving away from the probe reflects the incoming wave with a longer wavelength. Two Doppler shifts 1. between the probe and the moving blood cell (not shown here) 2. as the red blood cell reflects the ultrasound MOVING BLOOD CELL The ultrasound probe emits an ultrasound wave. A blood cell moving towards the probe reflects the incoming wave with a shorter wavelength. Doppler effect ULTRASOUND Shift in frequency directly related to the variation in frequency of the receptor and the cosine of the angle of incidence of the ultrasound beam. inversely proportional to the velocity of the sound in the tissue. Doppler imaging (ultrasound) Use BOTH normal ultrasound imaging and Doppler imaging. Used to image blood flow. 1. Doppler imaging looks at artery. 2. Get image and trace of blood flow. 3. This is a healthy artery. The flow is smooth and all in the same direction, like water in a large, slow river. Ultrasound in Medical Therapy Ultrasound, like any wave, carries energy that can be absorbed by the medium carrying it, producing effects that vary with intensity. When focused to intensities of 103 to 105 W/m2, ultrasound can be used to shatter gallstones or pulverize cancerous tissue in surgical procedures. Ultrasound in Medical Therapy Ultrasound treatment effective in reducing pain caused by certain injuries. Frequency range: 0.75 – 3 MHz Softening of tense muscles: 1. Sound waves penetrate specific muscle areas, causing warming. As a result, tight muscles become relaxed, providing relief from pain. 2. Ultrasound increases the blood flow to the affected area, thus allowing the proteins in the blood to repair themselves. Ultrasound in Interventional Radiology Valuable imaging technique for musculoskeletal pathology. Used for image- guided procedures such as aspiration of superficial or deep collections, injection of drugs, or biopsies. Ultrasonic Cavitation Ultrasonic or ultrasound cavitation is the use of ultrasound technology to break down fat cells. Involves: 1. Applying pressure on fat cells through ultrasonic vibrations. 2. The pressure makes the fat cells break down into a liquid form. 3. The body gets rid of it as waste through urine.