Question

16.24 resonances of the ear canal lead to increased sensitivity of hearing, as we've seen. Dogs have a much larger ear canal- 5.2 cm- than humans. What are the two lowest frequencies at which dogs have an increased in sensitivity? The speed of sound in the warm air of the ear is 350 m/s

A 1700 hz, 3400 hz
B 1700 hz, 5100 hz
C 3400, 6800 hz
3400, 10,200hz

Answer 1

The two lowest frequencies at which dogs have an increased sensitivity due to the resonances of their ear canal are approximately 1700 Hz and 5100 Hz.

Step-by-step explanation:

To calculate the lowest frequencies at which dogs have an increased sensitivity in hearing due to the resonance of their ear canal, we can use the following information:

• The speed of sound in warm air (37.0°C) is approximately 350 m/s.
• A dog's ear canal is approximately 5.2 cm or 0.052 m long.
• The ear canal behaves like a tube closed at one end.

The fundamental frequency and the first overtone for a tube closed at one end can be found using the formula:

∑f = v/(4L), where

• ∑f is the fundamental frequency or first harmonic
• v is the speed of sound
• L is the length of the ear canal

The first overtone or second harmonic is three times the fundamental frequency.

Therefore, the lowest resonant frequency (fundamental frequency) for a dog's ear canal is:

f = v/(4L) = 350 m/s / (4 * 0.052 m) = 1682.69 Hz ≈ 1700 Hz

And the first overtone is:

first overtone = 3 * ∑f = 3 * 1682.69 Hz = 5048.08 Hz ≈ 5100 Hz

Thus, the two lowest frequencies at which dogs have an increased sensitivity are approximately 1700 Hz and 5100 Hz.