Question 15 12 points save Answer Multipart. Loudspeakers for a rock concert are

Question

Question 15 12 points save Answer Multipart. Loudspeakers for a rock concert are placed 10 m apart at the front of a stage. The sound intensity front of these speakers (in front row) Is 1.27 x 10^-2 W/m^2. The front row Is 6 m from the stage. a) What is the decibel reading, d8, on a sound meter at the front row? The last row of the theater Is 94 m from the stage. b) What Is the sound intensity, I. at the last row? c) What Is the decibel reading, d8. at the back row? If a frequency of 512 Hz Is played from both speakers, and the temperature in the theater is 20 deg d) What is the wavelength of the sound wave?

Explanation / Answer

Note that

dB = 10log(I/Io)

where Io = 10^-12 W/m^2.

Here, I = 1.27E-2 W/m^2. Thus,

dB = 101 dB   [ANSWER, PART A]

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The last row is 96 m from the stage, 16 times farther.

As I varies with 1/r^2, then the intensity is 1/16^2 = 1/256 of the original.

Thus, at the back,

Iback = I/256 = 4.96E-5 W/m^2   [ANSWER, PART B]

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Using the same formula in A,

dB (back) = 76.96 dB   [ANSWER, PART C]

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Note that

v = 331 + 0.6T --->v = 343 m/s

As wavelength = v/frequency,

wavelength = 0.670 m    [ANSWER, PART D]

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