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Question

*** Please be sure to show work so I can learn this stuff.  And thank you for your help in advance.

A Speaker (which is to be treated as the source point) emits sound at a frequency of 4x10^3 Hz and a power of 28 Watts.  Your eardrum has a surface area of 0.5 cm^2 and you are standing 200 meters from the speaker.

a) What is the wavelength of this sound wave?

b) Leaving the amplitude as a variable, A, write the general wave equation for this sound wave.

c) What is the sound intensity at the speaker?

d) What is the power intercepted by your ear?

e) What is the soound intensity level, in decibels, at your ear from the speaker?

Explanation / Answer

a. wavelength L = velocity/frequency = 344/4000 = 0.086 m

b. general expression is pressure Amplitude Pmax = BKA

where B = bulk modulus, A = area, K= wave no= 2pi/L

c. Intensity = power/area = 28/0.5*10^-4 = 5.6 *10^5 W/m^2

d. power = I*area = 5.6*10^5 * 4pi * 200*200 = 2.813*10^11 Watts

e. intensity Level B = 10 dB log(i/io)

B = 10 dB log ( 2.8*10^11/10^-12)

B = 234.47 dB

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