Unit 4 Sound And Hearing

Unit 4 Sound and Hearing 4.0 Wave 4.1 Sound 4.2 Speed of sound, frequency and wavelength 4.3 Sound intensity and sound level 4.4 Resonance 4.5 Hearing 4.6 Effect of noise

4.0 Wave Mechanical waves 機 械 波 are generated by a disturbance such as a vibration, in a material medium. The wave is transmitted by particles moving back and forth in the medium. Examples of waves include waves on a rope or spring, water waves, and sound waves in air or other materials. A progressive or traveling wave 行波 is a disturbance which carries energy from one place to another without transferring matter. There are two types of progressive waves: transverse 橫波, and longitudinal 縱波. In a transverse wave, the disturbance of the particles is perpendicular to the direction the wave. In a longitudinal wave, the disturbance of the particles is parallel to the direction of the wave.

Wavelength 波長 Wavelength, represented by the Greek letter lambda (λ ), is the distance between two adjacent crests. Frequency 頻率 The frequency f is the number of waves generated per second. If a rope is jerked up and down twice per second, the frequency of the waves generated will be 2 hertz(Hz) (Hz is the unit for frequency). The frequency of a wave is the same as the frequency of its source. You can also find the frequency by counting how many crest pass through a fixed point in a second.

Speed The speed (v) of the wave is the distance moved by the crest or any point of the wave in 1 second. Amplitude 振幅 The amplitude (a) of the wave is the maximum height of the crest 波峰 , or the maximum depth of the trough 波谷, as measured from the resting (or equilibrium) position of the medium. Phase 相位 The arrows at A, B, C, and D show the vibration direction of the wave at these points. A and C are moving in the same direction at the same speed. They are in phase with each other. So are B and D. However, A and C are out of phase with B and D since they are moving in different directions. The wave equation The waves in the figure have a frequency of 3 Hz. This means that 3 wave crests will pass though P every second. A wave crest at P will be at Q one second later. If the wavelength(λ ) is 20cm, then the distance traveled by the crest in one second will be 60cm, the length of 3 wave crests. (20cm × 3 =60cm) Therefore the speed of the wave is 60cm/s.

v = fλ

speed of wave = frequency × wavelength :

4.1 Sound Sound is the disturbance of matter transmitted outwards from its source. Sound is a longitudinal wave. (a) When the vibrating string moves to the right, it compresses the air to the right and expands the air to the left(rarefaction 疏部). (b) When the string moves to the left, it compresses the air to the left, and causes a rarefaction on the right. (c) The vibrations cause a series of compressions 密部 and rarefactions that move out to generate sound waves. The amplitude of a sound wave decreases as it travels, because its energy is being spread out over a larger area. The sound wave is also absorbed by objects, as well as being converted to heat by the viscosity of air.

The compressions and rarefactions of a sound wave exert a net force on the eardrum, since it causes a pressure difference between atmospheric pressure and the pressure behind the eardrum. This causes the eardrum to vibrate. The vibrations are converted to nerve impulse, which are transmitted to the brain and allows the person to “hear” the sound.

4. 2 Speed, frequency and wavelength Pitch is the perceived frequency. A high pitch means a short wavelength. Larger musical instruments generate lower pitches. The speed of sound is affected by the temperature of the medium it is traveling in. For air at atmospheric pressure, vw = (331 m / s )

T (K ) 273 K

The speed of sound is usually not affected by frequency (from 20 to 20,000 Hz, which is human hearing range).

4.3 Sound intensity 聲強度 and sound level 聲級 Power is the energy in/out per unit time. It is measured in watts. Power =

Energy , 1 W= 1 J/s) time

The intensity of a wave is its power per unit area. It is measured in watts per meter squared (W/m2). I=

P A

The intensity of a wave is related to the square of its amplitude. The amplitude of a sound wave is related to the maximum pressure of the sound wave. The intensity level of sound is quoted in decibels 分貝(dB) instead of W/m2. This is related to how we perceive sound. Our ears respond proportionally to the changes in dB (or the logarithm of intensity), rather than the change in intensity itself.

The sound level β (unit: dB) of a sound wave having an intensity of I (unit: W/m2) can be calculated by the following equation. β (dB ) = 10 log 10

I I0

I0 = 10-12 W/m2 is a reference value. This is the smallest intensity (or the threshold intensity) of a 1000 Hz sound that can be detected by the human ear. The equivalent in dB is 0 since 10log101=0.

Example Find the dB value of a sound that has an intensity of 5.00×10-4 W/m2 (five times as intense as an 80.0dB sound) β (dB ) =10 log 10

I 5 ×10 −4 =10 log 10 I0 1×10 −12

= 87 .0dB

All sound differing by 7.00 dB will have a fivefold intensity difference. Example Show that if a sound has twice the intensity as another sound, it is 3 decibels higher in intensity.

β2 − β1 = 10 log 10

I2 = 10 log 10 2 = 10 × 0.301dB = 3.01dB I1

Since I2 and I1 can be replaced by any numbers, this result is true for any sound intensities that differ by a factor of two. For example a sound that is 53 dB is twice as intense as a sound that is 50dB.

4.4 Resonance 諧震 Interference and Standing wave When two or more waves arrive at the same point, they are superimposed on each other. If they arrive at the same point exactly in phase, they produce constructive interference 相長干涉. If they arrive at the same point exactly out of phase, they produce destructive interference 相消干涉.

When two waves coming from opposite directions are superimposed on each other, they produce a standing wave. A standing wave 駐波 alternates between destructive and constructive interference. A standing wave has nodes 波節 (places without movement or zero amplitude) and antinodes 波腹 (places of maximum amplitude).

Resonance at a air tube closed at one end If a tuning fork is placed in front of the open end of a tube, sound waves produced by the fork will travel into the tube, bounce off the closed end, and come back out. If the frequency of the tuning fork is just right, the waves going in and the waves going out will superimpose on each other to create a standing wave. The wavelength of the standing wave is 4 times the length of the tube(λ =4L). The node of the wave is at the closed end of the tube, and the antinode is at the open end. The frequency is: v v f = w = w λ 4L vw is the speed of the sound, and L is the length of the tube.

When the standing wave is produced, the wave is said to be produced at resonance. The tube “resonates” at this particular frequency. The frequency is called the resonant frequency. Standing waves with higher frequencies can be produced in the same tube. The frequencies of the standing waves which can be produced in a tube closed at one end can be found by the following formula: v f n = n w , n=1, 3, 5, … 4L The lowest frequency which produces the standing wave is called the fundamental 基頻 . The next lowest frequency that produces a standing wave is called the first overtone 泛音. All the resonant frequencies are called harmonics 諧音. Fundamental → 1st overtone → 2nd overtone →

1st harmonic 3nd harmonic 5rd harmonic

All the fundamentals and overtones produced in a tube with one closed end have their nodes at the closed end, and their antinodes at the open end. Example

(a) What length should a tube with one open end have if its fundamental frequency is to be 128 Hz (the C below middle C). Assume the temperature is 22.0°C. (b) What is the frequency of its fourth overtone? vw = 331 m / s

T (K ) 295 K = 331 m / s = 344 m / s 273 K 273 K

f9 = 9

L=

vw 344 m / s = = 0.672 m 4 f1 4(128 Hz )

vw = 9 f 1 = 1152 Hz 4L

Resonance at a air tube opened at both end The fundamental and first three overtures of a tube with ends open at both sides are shown. Antinodes occur at both open ends. A tube open at both ends has different resonant frequencies than a tube closed at one end.

4.5 Hearing Hearing is the perception of sound by the ear. Hearing is affected by several factors: 1. 2. 3.

pitch 音高 depends on the frequency of the sound wave loudness 響度 depends on the intensity and frequency of the sound timber 音質 depends on the number of different frequencies and their relative intensities

The ear can detect sounds within a certain range of frequencies and intensities. Frequency response The frequencies which an ear can detect depend on the sounds that can be resonated within the ear. The shorter hairs in the cochlea resonate at higher frequencies, while the longer hairs in the cochlea resonate at lower frequencies. The frequencies between which the hairs can resonate are from about 20 Hz to 20 kHz. This is the range of human hearing, although the upper limit decreases with age.

The dogs can hear sounds of up to 30 kHz which is considerably higher than what humans can hear. Dog whistles generate high frequency sounds which can only be detected by dogs. Sounds with frequencies above 20 kHz are called ultrasounds超聲波, and sounds with frequencies below 20 Hz are called infrasounds亞聲. The middle ear is a resonant cavity with resonances between 700-1500 Hz. A standing wave can be generated within the ear canal (auditory canal) of the outer ear. The ear canal is similar to a tube with one closed end. It is approximately 2.5 cm long and can contain a standing wave with a wavelength of 4 × 2.5 cm =10cm. Its node will be at the ear drum and the antinode at the pinna耳廓. Waves with this particular wavelength can be heard at lower intensities since a greater pressure difference is generated due to resonance.

Since the speed of sound is about 330m/s, the frequency of the standing wave will be around 3300Hz. f =

v

λ

=

330 m / s = 3300 Hz 0.1m

The different resonant frequencies in the ear mean that the lowest intensity that can be heard by the ear is not the same for all frequencies. For example, because of resonance in the outer ear, sounds with frequencies of about 3 kHz can be heard at lower intensities. Intensity response An increase in the intensity of the sound being heard is perceived by the brain as an increase in loudness. An increase in the perceived loudness is caused by: • greater stimulation of nerve endings caused by the greater vibration of the hairs in the cochlea • stimulation of more nerve endings caused by the greater vibration of the hairs in the cochlea • higher stimulation thresholds of the nerve cells being activated How loud a sound seems to a person is affected by many factors. How loud a sound seems may vary from person to person. Loudness is subjective. However, intensity is a measurable physical quantity defined by the energy per second per m2 of cross-sectional area. Sound intensity and sound levels of some sounds

Loudness is a person’s subjective perception of the volume of a sound. A person is sensitive to logarithmic changes in loudness (just like in intensity). The loudness of a sound at any single intensity is dependant on its frequency.

Each line is a single level of loudness. Loudness is measured in phon 方. The phon value of a sound at a particular frequency is equivalent to the decibel value of a 1 kHz sound that is perceived to have the same loudness. For example, if a 400Hz sound feels as loud as a 30dB 1kHz sound, the loudness of the 400Hz sound is 30 phon.

The shaded area represents the phon level of normal conversation. The 0 phon line is the hearing threshold 聽覺閾 of a normal person. The other two lines represent the hearing thresholds of persons with varying degrees of hearing disabilities.

Threshold intensity is the minimum intensity of a sound that can be heard by a person at a certain frequency. The threshold intensity of a 3 kHz sound is -8dB for a person with normal hearing.

4.6 Effect of noise Noise is made up of many sounds of different frequencies, each with different amplitudes. Noise can have different effects on different people. A particular noise may be too loud for one person, but acceptable to another. The total absence of noise can also be very disturbing. The level of damage to the ear increases with the noise level. A noise level of 85 dB and above is generally unacceptable.

Hearing ability naturally decreases with age. This is called presbycusis 老年失聰. The green curves show the hearing losses at different frequencies of a forty year old and a sixty year old. The people with the hearing losses represented by the green curves have not been exposed to excessively loud noises. Note that there is a greater hearing loss for the higher frequencies. A hearing loss of 20 dB means that the threshold of hearing for that particular frequency is 20 dB greater than that of a normal person. This would be marked on the graph as -20dB on the y-axis. The red curves show the hearing losses of two people, aged 40 and 65, who have been exposed to noise levels over 95 dB in their work. This shows why there is legislation that limits the noise level in workplaces. Ear protection (earplugs and/or earmuffs) should be worn when the noise level cannot be kept down. Discos and clubs should have health hazard warnings. Loud noises may also cause tinnitus耳鳴, which is a temporary or permanent ringing sound in the ears. A person with tinnitus may find it hard to hear what other people are saying, especially if there is background noise. Other effects of noise include: 1 feelings of annoyance 2 inability to think clearly 3 dizziness or sickness (> 125 dB) 4 pain in the ears (> 130 dB) 5 permanent deafness (~ 190 dB, short-term exposure)

Checklist 4.0 Wave • describe the production of pulses and progressive transverse wave on ropes, springs and ripple tanks • recall the meaning of wavelength, frequency, speed, amplitude and phase • represent a transverse wave on a displacement-distance graph and extract information from it • recall the wave equation v=fλ and use it to solve problems 4.12 Sound • recall the properties of sound and how sound is generated and received. 4.2 Speed of sound, frequency and wavelength • simple calculation using wave equation • recall the relationship between pitch and frequency • the speed of sound is affected by the temperature and it’s equation 4.3 Sound intensity and sound level • definition of intensity • definition of decibels (dB) and the related calculation • recall the reference intensity in the definition of dB • why dB is chosen as the unit for sound level measurement • recall some typical sound levels 4.4 Resonance • sketch the resonance of air in a tube closed at one end and open at both ends • recall the definition of fundamental, overtones and harmonics • calculation related with the wavelength and the length of a tube when resonance is happened 4.5 Hearing • state the relationship between perception (pitch, loudness and timbre) and their corresponding physical quantities. • understand the base of frequency response of the ear • why at 3 kHz frequency, sound can be better heard? • recall the frequency range for the normal hearing • recall the frequencies for ultrasound and infrasound • understand the difference between loudness and intensity • understand the loudness vs. frequency curves • recall measurement of and unit of loudness 4.6 Effect of noise • limit of the acceptable sound level • recall the long term effect of noise • other effects of noise and possible protection measures