Frequency response of the human ear

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Normal human ears detect pressure waves in air. These waves have frequencies that  vary from 20 Hz to 20 kHz. The chart to the right shows the sensitivity of a normal human ear, and can be interpreted as follows. On the horizontal axis is the frequency of a given wave. The vertical axis records the size of the response in the human ear excited by a wave of that frequency, at a fixed, reference amplitude. The higher the curve, the more strongly the internal mechanisms of the human ear respond. A wave with frequency 3 kHz is most easily detected by a normal human ear. Such a wave has the pitch of a vigorously crying infant.  

Do

1. An adult ear canal is about one inch deep. A standing wave that is resonant in this open cavity has a wavelength about four times greater. Assuming we evolved so that our hearing is optimally attuned to detect the vigorous cry of a baby, estimate the speed of sound in air. (Do not worry about whether evolution actually worked this way.)

2. Most people perceive integer multiples of frequencies to be harmonious. Two waves whose frequencies are in the ratio 3:2 are perceived to be an interval of a “fifth”, an interval that is prominently featured in the soundtracks of 2001: A Space Odyssey and Star Wars. On a copy of the figure above, clearly label the vertical line that corresponds to the frequency 200 Hz with the letter “G” and the frequency that is an interval of one “fifth” above it as “D.”

3. Consider the figure to the right in place of the figure in part 1. If the solid curve were now the total response of your left ear to pressure waves at the fixed, reference amplitude (instead of the actual response shown above), and if the dashed curve were the total response of your right ear, your perception of sound would be very different. Think about the physics of waves and about the information that you could discern with this unusual model of hearing, then briefly propose and explain three significant differences from normal in the way you would perceive sound.

Bill Dorland 4/19/18