Chapter 17: Physics of Hearing PDF

Chapter 17: Physics of Hearing Mrs. Pooja Brahmaiahchari Introduction Sound is a disturbance of the atoms in matter transmitted from its origin outward (in other words, a wave). Such a wave is the physical phenomenon we call SOUND. Its perception is Hearing. Sound Soun...

Chapter 17: Physics of Hearing Mrs. Pooja Brahmaiahchari Introduction Sound is a disturbance of the atoms in matter transmitted from its origin outward (in other words, a wave). Such a wave is the physical phenomenon we call SOUND. Its perception is Hearing. Sound Sound has important applications beyond hearing. Ultrasound, for example, is not heard but can be employed to form medical images and is also used in treatment. The physical phenomenon of sound is defined to be a disturbance of matter that is transmitted from its source outward. Sound is a wave. On the atomic scale, it is a disturbance of atoms that is far more ordered than their thermal motions.  In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. As the string oscillates back and forth, it transfers energy to the air, mostly as thermal energy created by turbulence. But a small part of the string’s energy goes into compressing and expanding the surrounding air, creating slightly higher and lower local pressures.  These compressions (high pressure regions) and rarefactions (low pressure regions) move out as longitudinal pressure waves having the same frequency as the string—they are the disturbance that is a sound wave. Sound waves in air and most fluids are longitudinal, because fluids have almost no shear strength. In solids, sound waves can be both transverse and longitudinal.  The amplitude of a sound wave decreases with distance from its source, because the energy of the wave is spread over a larger and larger area. But it is also absorbed by objects, such as the eardrum and converted to thermal energy by the viscosity of air. In addition, during each compression a little heat transfers to the air and during each rarefaction even less heat transfers from the air, so that the heat transfer reduces the organized disturbance into random thermal motions. Speed of Sound, Frequency and Wavelength Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can also directly sense the frequency of a sound. Perception of frequency is called PITCH. The wavelength of sound is not directly sensed, but indirect evidence is found in the correlation of the size of musical instruments with their pitch.  High pitch means small wavelength, and the size of a musical instrument is directly related to the wavelengths of sound it produces. The relationship of the speed of sound, its frequency, and wavelength is the same as for all waves: 𝑣𝑤 = 𝑓𝜆 where 𝑣𝑤 is the speed of sound, f is its frequency, and 𝜆 is its wavelength.  The wavelength of a sound is the distance between adjacent identical parts of a wave—for example, between adjacent compressions as illustrated in Figure (previous slide). The frequency is the same as that of the source and is the number of waves that pass a point per unit time. The speed of sound in a medium is determined by a combination of the medium’s rigidity (or compressibility in gases) and its density. The more rigid (or less compressible) the medium, the faster the speed of sound.  The speed of sound in air is low, because air is compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases. Earthquakes, essentially sound waves in Earth’s crust, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes have both longitudinal and transverse components, and these travel at different speeds.  The speed of sound is affected by temperature in a given medium. For air at sea level, the speed of sound is given by 𝑇 𝑣𝑤 = (331𝑚/𝑠) 273 𝐾 where the temperature (denoted as T) is in units of kelvin.  The speed of sound in gases is related to the average speed of particles in the gas, 𝑣𝑟𝑚𝑠 , and that 3𝑘𝑇 𝑣𝑟𝑚𝑠 = 𝑚 Where k is the Boltzmann constant ( 1.38 x 10-23 J/K) and m is the mass of each (identical) particle in the gas. So, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature.  One of the more important properties of sound is that its speed is nearly independent of frequency. This independence is certainly true in open air for sounds in the audible range of 20 to 20,000 Hz. Because they travel at the same speed in a given medium, low- frequency sounds must have a greater wavelength than high frequency sounds. Here, the lower-frequency sounds are emitted by the large speaker, called a woofer, while the higher-frequency sounds are emitted by the small speaker, called a tweeter. 1. What frequency sound has a 0.10-m wavelength when the speed of sound is 340 m/s? 2. Calculate the speed of sound on a day when a 1500 Hz frequency has a wavelength of 0.221 m. 3. Show that the speed of sound in 20oC air is 343 m/s, as claimed in the text. Sound Intensity and Sound Level Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity is 𝑃 𝐼= 𝐴 Where P is the power through an area A. The SI unit for Intensity I is W/m2.  The intensity of a sound wave is related to its amplitude squared by the following relationship: ∆𝑝 2 𝐼= 2ρ𝑣𝑤 Here ∆𝑝 is the pressure variation or pressure amplitude in units of pascals (Pa) or N/m2.  Sound intensity levels are quoted in decibels (dB) much more often than sound intensities in watts per meter squared. Decibels are the unit of choice in the scientific literature as well as in the popular media. The sound intensity level in decibels of a sound having an intensity in watts per meter squared is defined to be 𝐼 𝛽 𝑑𝐵 = 10 log10 ( ) 𝐼0 where 𝐼0 = 10−12 W/m2 is a reference intensity.  In particular, 𝐼0 is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone. −12 𝑊 The decibel level of a sound having the threshold intensity of 10 𝑚2 is β = 0, because log10 1 = 0. That is, the threshold of hearing is 0 decibels. 4. A sound wave traveling in 20oC air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave? 5. What sound intensity level in dB is produced by earphones that create an intensity of 4.00 x 10-2 W/m2? Doppler Effect and Sonic Booms The characteristic sound of a motorcycle buzzing by is an example of the Doppler effect. The high-pitch scream shifts dramatically to a lower-pitch roar as the motorcycle passes by a stationary observer. The closer the motorcycle brushes by, the more abrupt the shift. The faster the motorcycle moves, the greater the shift. We also hear this characteristic shift in frequency for passing race cars, airplanes, and trains.  The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer. The actual change in frequency due to relative motion of source and observer is called a Doppler shift. The Doppler effect and Doppler shift are named for the Austrian physicist and mathematician Christian Johann Doppler (1803–1853), who did experiments with both moving sources and moving observers.  What causes the Doppler shift? Figures compare sound waves emitted by stationary and moving sources in a stationary air mass. Each disturbance spreads out spherically from the point where the sound was emitted.  The same effect is produced when the observers move relative to the source. Motion toward the source increases frequency as the observer on the right passes through more wave crests than she would if stationary. Motion away from the source decreases frequency as the observer on the left passes through fewer wave crests than he would if stationary.  For a stationary observer and a moving source, the frequency 𝑓𝑜𝑏𝑠 received by the observer can be shown to be 𝑣𝑤 𝑓𝑜𝑏𝑠 = 𝑓𝑠 𝑣𝑤 ± 𝑣𝑠 where 𝑓𝑠 is the frequency of the source, 𝑣𝑠 is the speed of the source along a line joining the source and observer, and 𝑣𝑤 is the speed of sound. The minus sign is used for motion toward the observer and the plus sign for motion away from the observer, producing the appropriate shifts up and down in frequency. Note that the greater the speed of the source, the greater the effect. Similarly, for a stationary source and moving observer, the frequency received by the observer is given by 𝑣𝑤 ± 𝑣𝑜𝑏𝑠 𝑓𝑜𝑏𝑠 = 𝑓𝑠 𝑣𝑤 6) (a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed? 7) What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s. The Doppler effect is observed when: A. The source of sound is stationary, and the observer is moving B. The source of sound is moving, and the observer is stationary. C. Both source and observer are moving relative to each other. D. Any of the above situations Sonic Booms to Bow Wakes Sound waves from a source that moves faster than the speed of sound spread spherically from the point where they are emitted, but the source moves ahead of each.  There is constructive interference along the lines shown (a cone in three dimensions) from similar sound waves arriving there simultaneously. This superposition forms a disturbance called a sonic boom, a constructive interference of sound created by an object moving faster than sound. Inside the cone, the interference is mostly destructive, and so the sound intensity there is much less than on the shock wave. An aircraft creates two sonic booms, one from its nose and one from its tail.  Sonic booms are one example of a broader phenomenon called bow wakes. A bow wake, such as the one in Figure, is created when the wave source moves faster than the wave propagation speed. Water waves spread out in circles from the point where created, and the bow wake is the familiar V-shaped wake trailing the source. Sound Interference and Resonance Interference is the hallmark of waves, all of which exhibit constructive and destructive interference exactly analogous to that seen for water waves. In fact, one way to prove something “is a wave” is to observe interference effects. So, sound being a wave, we expect it to exhibit interference;  Headphones designed to cancel noise with destructive interference create a sound wave exactly opposite to the incoming sound. These headphones can be more effective than the simple passive attenuation used in most ear protection. Such headphones were used on the record-setting, around the world nonstop flight of the Voyager aircraft to protect the pilots’ hearing from engine noise. Where else can we observe sound interference? All sound resonances, such as in musical instruments, are due to constructive and destructive interference. Only the resonant frequencies interfere constructively to form standing waves, while others interfere destructively and are absent.  Suppose we hold a tuning fork near the end of a tube that is closed at the other end, as shown in Figure. The figures show how a resonance at the lowest of these natural frequencies is formed. A disturbance travels down the tube at the speed of sound and bounces off the closed end.  Resonance of air in a tube closed at one end, caused by a tuning fork. The disturbance reflects from the closed end of the tube. This interference forms a standing wave, and the air column resonates.  Resonance of air in a tube closed at one end, caused by a tuning fork. The standing wave formed in the tube has its maximum air displacement (an antinode) at the open end, where motion is unconstrained, and no displacement (a node) at the closed end, where air movement is halted. The distance from a node to an antinode is one-fourth of a wavelength, and this equals the length of the tube; This standing wave has one-fourth of its wavelength in the tube, so that 𝜆 = 4𝐿.  Given that maximum air displacements are possible at the open end and none at the closed end, there are other, shorter wavelengths that can resonate in the tube Here the standing wave has three-fourths of 3 its wavelength in the tube, 𝐿 = ( )𝜆′ 4 4𝐿 so that 𝜆′ = 3  We use specific terms for the resonances in any system. The lowest resonant frequency is called the fundamental, while all higher resonant frequencies are called overtones. All resonant frequencies are integral multiples of the fundamental, and they are collectively called harmonics. The fundamental is the first harmonic, the first overtone is the second harmonic, and so on.  Hence the resonant frequencies of a tube closed at one end are: 𝑣𝑤 𝑓𝑛 = 𝑛 , 𝑛 = 1,3,5 4𝐿 Where f1 is the fundamental, f3 is first overtone and so on. 8. a) What length should a tube closed at one end have on a day when air temperature is 22oC. If its fundamental frequency is to be 128 Hz? b) What is the frequency of its fourth overtone? How many nodes and antinodes does a second overtone of closed pipe consists of?  Another type of tube is one that is open at both ends. Examples are some organ pipes, flutes, and oboes. The resonances of tubes open at both ends can be analyzed in a very similar fashion to those for tubes closed at one end. The air columns in tubes open at both ends have maximum air displacements at both ends,  Based on the fact that a tube open at both ends has maximum air displacements at both ends, we can see that the resonant frequencies of a tube open at both ends are: 𝑣𝑤 𝑓𝑛 = 𝑛 , 𝑛 = 1,2,3 …. 2𝐿 where f1 is the fundamental, f2 is the first overtone, f3 is the second overtone, and so on. 9. How long must a flute be in order to have a fundamental frequency of 262 Hz on a day when air temperature is 20oC? 10. What will be the fundamental frequency and first three overtones for a 26cm long organ pipe at 20oC if it is a) open and b) closed? 11. Calculate the sound intensity level in decibels for a sound wave travelling in air at 0oC and having a pressure amplitude of 0.656 pa. (given the density of 1.29 kg/m3 at atmospheric pressure at 0oC) Hearing Hearing is the perception of sound. Normal human hearing encompasses frequencies from 20 to 20,000 Hz, an impressive range. Sounds below 20 Hz are called infrasound, whereas those above 20,000 Hz are ultrasound. Neither is perceived by the ear, although infrasound can sometimes be felt as vibrations.  Dogs can hear sounds as high as 30,000 Hz, whereas bats and dolphins can hear up to 100,000-Hz sounds. Elephants are known to respond to frequencies below 20 Hz. The perception of frequency is called pitch. Most of us have excellent relative pitch, which means that we can tell whether one sound has a different frequency from another. Typically, we can discriminate between two sounds if their frequencies differ by 0.3% or more.  The ear is remarkably sensitive to low-intensity sounds. The lowest audible intensity or threshold is about 10-12 W/m2 or 0 dB. Sounds as much as 1012 more intense can be briefly tolerated. Very few measuring devices are capable of observations over a range of a trillion. The perception of intensity is called loudness. The ear has its maximum sensitivity to frequencies in the range of 2000 to 5000 Hz, so that sounds in this range are perceived as being louder than, say, those at 500 or 10,000 Hz, even when they all have the same intensity.  We call our perception of these combinations of frequencies and intensities tone quality, or more commonly the timbre of the sound. A unit called a Phon is used to express loudness numerically. Phons differ from decibels because the Phon is a unit of loudness perception, whereas the decibel is a unit of physical intensity. Hearing losses can occur because of problems in the middle or inner ear. Conductive losses in the middle ear can be partially overcome by sending sound vibrations to the cochlea through the skull.  Hearing aids for this purpose usually press against the bone behind the ear, rather than simply amplifying the sound sent into the ear canal as many hearing aids do. Damage to the nerves in the cochlea is not repairable, but amplification can partially compensate.  There is a risk that amplification will produce further damage. Another common failure in the cochlea is damage or loss of the cilia but with nerves remaining functional. Cochlear implants that stimulate the nerves directly are now available and widely accepted. Over 100,000 implants are in use, in about equal numbers of adults and children. The cochlear implant was pioneered in Melbourne, Australia, by Graeme Clark in the 1970s for his deaf father. The implant consists of three external components and two internal components.  The external components are a microphone for picking up sound and converting it into an electrical signal, a speech processor to select certain frequencies and a transmitter to transfer the signal to the internal components through electromagnetic induction. The internal components consist of a receiver/ transmitter secured in the bone beneath the skin, which converts the signals into electric impulses and sends them through an internal cable to the cochlea and an array of about 24 electrodes wound through the cochlea. These electrodes in turn send the impulses directly into the brain. The electrodes basically emulate the cilia. 10. A closed organ pipe (closed at one end) is excited to support the first overtone. It is found that air in the pipe has, A. Three nodes and three antinodes B. Two nodes and four antinodes C. Two nodes and Two antinodes D. Four nodes and four antinodes THANK YOU