Resonances of the ear canal lead to increased sensitivity of hearing, as we've seen. Dogs have a much longer ear canal-5.2 cm-than humans. What are the two lowest frequencies at which dogs have an increase 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 Hz, 6800 Hz

D. 3400 Hz, 10,200 Hz

B. 1700 Hz, 5100 Hz

Explanation:

Parameters given:

Length of ear canal = 5.2cm = 0.052 m

Speed of sound in warm air = 350 m/s

The ear canal is analogous to a tube that has one open end and one closed end. The frequency of standing wave modes in such a tube is given as:

f (m) = m * (v/4L)

Where m is an odd integer;

v = velocity

L = length of the tube

Hence, the two lowest frequencies at which a dog will have increased sensitivity are f (1) and f (3).

f (1) = 1 * [350 / (4*0.052) ]

f (1) = 1682.69 Hz

Approximately, f (1) = 1700 Hz

f (3) = 3 * [350 / (4*0.052) ]

f (3) = 5048 Hz

Approximately, f (3) = 5100 Hz