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The physics of the ear questions
The ear responds to a range of intensities spanning about twelve orders of magnitude, which no linear scale can display. This topic covers how the outer, middle and inner ear transmit sound, why intensity is measured in decibels, and how the dBA weighting matches the measurement to what the ear actually hears.
17 original questions · 51 marks · the physics of the ear notes · Medical physics
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State what is meant by the intensity of a sound wave, give the equation defining it, and state its unit.
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Intensity is the power carried by the wave through unit area at right angles to its direction of travel (1). I = P/A, measured in W m−2 (1).State what is meant by the threshold of hearing, and give its value.
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The minimum intensity that a normal ear can detect, quoted at a frequency of 1 kHz (1). Its value is I0 = 1.0 × 10−12 W m−2 (1). The frequency is part of the definition, and answers that omit it lose the mark.Describe the path taken by a sound from the air outside the ear to the nerve impulses that leave it, naming the outer, middle and inner sections.
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Outer ear: the pinna collects the sound and funnels it along the ear canal to the eardrum, which vibrates (1). Middle ear: the three ossicles carry the vibration from the eardrum across to the smaller oval window. Inner ear: the oval window drives the fluid in the cochlea, where hair cells convert the vibration into nerve impulses (1).State what an equal loudness curve shows, and state what quantity is plotted on each axis.
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It joins the combinations of frequency and intensity level that a listener judges to be equally loud (1). Intensity level in dB is plotted against frequency, on a logarithmic frequency axis (1).Calculate the intensity level of a sound of intensity 1.0 × 10−6 W m−2.
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Intensity level = 10 log(I/I0) = 10 log[(1.0 × 10−6)/(1.0 × 10−12)] (1) = 10 log(106) = 60 dB (1).State the approximate range of frequencies that a healthy young person can hear.
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About 20 Hz to 20 kHz (1). The upper limit falls with age long before the lower one does.A sound has an intensity of 3.0 × 10−5 W m−2. Calculate its intensity level.
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I/I0 = (3.0 × 10−5)/(1.0 × 10−12) = 3.0 × 107 (1). Intensity level = 10 log(3.0 × 107) (1) = 75 dB (1).A sound is measured at 85 dB. Calculate its intensity.
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85 = 10 log(I/I0), so I/I0 = 108.5 (1) = 3.16 × 108 (1). I = 3.16 × 108 × 1.0 × 10−12 = 3.2 × 10−4 W m−2 (1).A tone of intensity level 66 dB falls on an eardrum of cross-sectional area 55 mm2. Calculate the power incident on the eardrum.
Explain how the middle ear increases the pressure of the vibration reaching the inner ear, and state why this increase is necessary.
Sound A has an intensity of 4.0 × 10−6 W m−2 and sound B an intensity of 8.0 × 10−5 W m−2. Calculate how many decibels louder B is than A.
Explain why sound is measured on a logarithmic scale rather than a linear one.
Describe how an equal loudness curve is produced.
On an equal loudness curve, a tone of frequency 100 Hz has to be at an intensity level of 60 dB to sound as loud as a 1 kHz tone at 30 dB. Calculate the ratio of the intensity of the 100 Hz tone to that of the 1 kHz tone, and explain what this shows about the ear. State where on such a curve the ear is most sensitive.
A machine in a workshop produces an intensity level of 92 dB at a bench. A second, identical machine is switched on beside it. Calculate the new intensity level at the bench, and determine how many such machines would be needed to raise the level to 102 dB.
A worker is exposed to a noise of 96 dBA. Ear defenders reduce the intensity reaching the ear by a factor of 250. Calculate the intensity level inside the defenders, and explain why a workplace noise limit is written in dBA rather than in dB.
Compare the equal loudness curves of a person with normal hearing with those of a person who has spent years working in a noisy factory, and explain the practical difficulty the second person is likely to report.
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