Loudspeakers for a rock concert are placed 30 m apart at the front of a stage. A

Question

Loudspeakers for a rock concert are placed 30 m apart at the front of a stage. A decibel meter records 100 dB at the front row seats directly in front of each speakers. The front row is 3 m from the stage.

a) The sound intensity, I, at the front row is ______ W/m2.

The last row of the theater is 50 m from the stage.

b) The sound intensity, I, at the last row is ______ W/m2

c) The decibel reading, dB, at the last row is ______.

If a frequency of 440 Hz is played from both speakers, and the temperature in the theater is 25 deg C

d) The wavelength of the sound wave is ______.

Explanation / Answer

(A) sound level = 10 log(I/I0)

where I0 = 10^-12 W/m^2

100 = 10 log(I/10^-12)

I = 0.01 W/m^2

(B) suppose power of each speaker is P then .

I = P/(4pi 3^2) + P/(4pi(3^2 + 30^2))

P/4pi = 0.11221

now for last row,

I = P/(4pi 50^2) + P(4pi (50^2 + 30^2))

I = (P/4pi) (6.94 x 10^-4)

I = (0.11221)(6.94 x 10^-4) = 7.79 x 10^-5 w/m^2

(c) Sound Level = 10 log(I/I0)

     = 10 log( (7.79 x 10^-5) / 10^-12) = 78.9 dB

(D) v = 343 m/s (Speed of sound)

f = 440 Hz

wavelength = v / f = 343/440 = 0.78 m

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