In this problem, you will estimate the smallest kinetic energy of vibration that the human ear can detect. Suppose that a harmonic sound wave at the threshold of hearing (I = 1.0 × 10−12 W/m 2) is incident on the eardrum. The speed of sound is 340 m/s and the density of air is 1.3 kg/m 3.
(a) What is the maximum speed of an element of air in the sound wave?
(b) Assume the eardrum vibrates with displacement s0 at angular frequency (; its maximum speed is then equal to the maximum speed of an air element. The mass of the eardrum is approximately 0.1 g. What is the average kinetic energy of the eardrum?
(c) The average kinetic energy of the eardrum due to collisions with air molecules in the absence of a sound wave is about 10−20 J. Compare your answer with (b) and discuss.