Question

Sound 1 or sound 2 can be played through a speaker.

A) Sound 1 has a sound level(B1) that is 9dB greater than the sound level(B2) of sound 2. What is the relationship between the intensity of sound 1 and the intensity of sound 2?

B) The sound level(B1) of sound 1 is 2 times the sound level (B2) of sound 2. What is the relationship between the intensity of sound 1 and the intensity of sound 2?

C) A 210-W speaker is mounted on top of a tall pole at an outdoor concert and sound is delivered uniformly im all directions. What is the sound level you hear when you are 3.9m from the speaker?

D) Is the sound in part (C) painfully loud, loud, somewhat loud, or not too loud?

Answer 1

A)

B1 - B2 = 9

10*log(I1/Io) - 10*log(I2/Io) = 9

10*log(I1) - 10log(Io) - 10*log(I2) + 10*logIo = 9

10*log(I1) - 10*log(I2) = 9

10*log(I1/I2) = 9

I1/I2 = 8

I1 = 8*I2

Intensity of sound 1 is 8 times grater than intensity of sound 2

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B)

B1 = 2*B2

10*log(I1/Io) = 2*10*log(I2/Io)

log(I1/Io) = 2*log(I2/Io)

logI1 - logIo = 2*logI2 - 2*logIo

log(I1/I2^2) = -log(Io)

I1/I2^2 = 1/Io = 10^12

I1 = I2^2*10^12

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C)

Intensity I = P/(4*pi*r^2)

I = 210/(4*pi*3.9^2)

I = 1.1 W/m2

intensity level = 10*log(I/Io)

B = 10*log(1.1/10^-12)

B = 120 dB

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D)

painfully loud