To decrease the intensity of the sound you are hearing from yourspeaker system b

Question

To decrease the intensity of the sound you are hearing from yourspeaker system by a factor of 36, you can
reduce theamplitude by a factor of 12 and increase your distance from thespeaker by a factor of 3.
reduce theamplitude by a factor of 4 and increase your distance from thespeaker by a factor of 3.
reduce theamplitude by a factor of 2 and increase your distance from thespeaker by a factor of 3.
reduce theamplitude by a factor of 3 and increase your distance from thespeaker by a factor of 4.
reduce theamplitude by a factor of 3 and increase your distance from thespeaker by a factor of 12.

Explanation / Answer

original intensity = I, decreased intensity I' = I/36, so I/I' =36 original amplitude = Ao, reduced amplitude =Ao' = Ao/a (a > 1), soAo/Ao' = a original distance = d, increased distance = d' = bd (b > 1), sod'/d = b intensity I = A22v/2, where A =Ao/d I =Ao22v/(2d2)        (1) then I' =Ao'22v/(2d'2)   (2) (1)/(2): 36 = a2*b2 a*b = 6 the answer is reduce the amplitude by a factor of 2 and increase your distancefrom the speaker by a factor of 3. (because 2*3 = 6)

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