Question

3. A sinusoidal sound wave arrives at an ear, at time zero, the pressure on the eardrum is a maximum and the nearest pressure minimum is 0.45 meters away. The difference in pressure between the two locations is 0.60 Pa. a) What is the frequency of this sound? b) Find the intensity of the sound. c) How much energy does the sound wave deliver to the eardrum in one minute if the eardrum's area is 70 square millimeters?

Answer 1

Given p_max - p_min = 0.6 Pa lambda = 0.9 in V = 343 m/s (a) frequency (f) v = v/lambda = 343/0.9 = 381.1 Hz (b) Intensity (I) I = (delta p)^2/2 pv Here, delta p = p_max - p_min/2 = 0.6/2 = 0.3 Pa p = density of sir = 1.225 kg/m^3 r = 343 m/s \r\n I = (0.3)^2/2 times 1.225 times 343 watt/m^2 I = 1.02 times 10^negative 4 watt/m^2 (c) Energy t = 60 s A = 70 mm^2 Energy = P times t P = I times A (watt rightarrow E = PAE Energy = 1.07 times 10^negative 4 times 70 times (10^negative 3)^2 times 60 E = 4.498 times 10^negative 7 joule