The effects of ear canal acoustics on hearing ability

Reason for the Correct Answer:

The positions of nodes and antinodes determine the constraints on wave frequencies in most harmonic systems

Waves with maxima/minima at the closed end would be rapidly absorbed

Waves with minima at the open end would fail to fully exploit the resonance of the cavity

Standing waves in the ear canal should have a minimum at the sealed end and a maximum at the open end.

Waves are most strongly amplified when they have a node at the end of the ear and an antinode at the opening.

Reason for the Correct Answer:

The wavelength of a sound wave times its frequency gives its speed.

For a tube sealed at one end, the allowed frequencies are those corresponding to a sine wave with a node at the sealed end and a peak at the open end

Only one answer choice will satisfy these boundary conditions

The longest-wavelength sine wave that satisfies the boundary conditions has frequency 𝒗/4L

Reason for the Correct Answer:

As noted in the passage, a peak on the graph for a given loudness (in phons) corresponds to reduced sensitivity to that frequency.

A minimum on the graph corresponds to increased sensitivity to sounds of a given intensity.

The 2000-5000 Hz  portion of the graph is generally a minimum region for all perceived loudnesses plotted.

The minimum region means that, for point on the graph defined by a given sound level (in dB) and a given frequency, a higher-loudness curve will pass through the point than would in the absence of a minimum.

Patients perceive sounds as louder when they are in the 2000-5000 Hz range.

Reason for the Correct Answer:

The amplitude versus displacement graph for a sound wave is a sine wave, but the waves themselves are radially symmetric as they pass into the ear—-so there should not be any asymmetric tissue fatigue.

While a softer ear canal could affect resonance frequencies, this is not a large effect and it should not greatly change the number of resonance frequencies in the frequency range of interest.

If passing waves are more easily able to deform the ear canal, it will absorb more of their energy and dissipate it

A softer ear canal would reduce hearing sensitivity due to absorption of the sound waves.

Reason for the Correct Answer:

Capped tubes have multiple resonance frequencies.

On the graph, a resonance is responsible for the minimum in the 1000-5000 Hz region on each of the equal-loudness curves

The higher-order resonant frequencies are given by integer multiples of the fundamental frequency

Thus 4000 x 3 Hz = 12000 Hz should represent a resonant frequency for the tube

The capped tube model would predict an additional loudness-curve minimum at 12000 Hz.