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# The effects of ear canal acoustics on hearing ability

## Problem

The acoustic properties of the human ear canal can be predicted by modeling the ear as a rigid tube that has been sealed at one end (Figure 1). Such a tube naturally amplifies sounds that are at or near its resonant frequencies, and it dampens sounds distant from its natural frequencies---the closer a given frequency lies to the resonant frequency of the tube, the more it will be amplified. The physical mechanism for this effect is the formation of standing waves in the tube as sounds enter the ear, pass to the end, and then reflect off the wall back towards the entry point. As a result of this effect, the perceived intensity of a given sound frequency often does not match its actual intensity before it enters the ear canal. This effect is deliberate on the part of the body, and it allows humans to retain maximum sensitivity to particular sounds, like speech.
This effect is observable in equal-loudness curves (Figure 2). The x axis gives the frequency of a given sound (in Hz), the y axis gives the laboratory-measured amplitude of the sound waves (in dB, or decibels), and the separate curves correspond to the perceived “loudness” of sounds with a given frequency and amplitude, as reported by a human observer. The units for loudness are called “phons.” The perceived loudness of a sound can be found by finding the point on the graph corresponding to the given frequency and intensity (in dB) of the sound, and then finding the equal-loudness curve that lies closest to that point and recording its corresponding loudness level (in phons). Thus, for a given perceptual loudness curve, a peak corresponds to a frequency that the ear canal filters out, such that a higher intensity is needed to reach a given perceived loudnessminus, minus, minusresulting in human hearing being less sensitive to that frequency.
Figure 1: A simple model of the ear canal as a tube with an opening at one end.
Figure 2: A set of equal-loudness curves for a typical human (OSHA, 2014).
Which of the following properties describes the wave patterns most strongly amplified by the ear canal?