Question

The sound produced by an outdoor rock concert is 120 dB when measured 1 m from the sound source (the speakers). If the sound propagates radially outward through a non-absorbing medium, how far away do you need to be before the sound is half as loud?

Group of answer choices

500 m

1000 m

100 m

1,260 m

2000 m

Answer 1

Loudness of sound is given by,

L = 10*log(I/I0)

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

I0 = 10^-12 W/m^2

at 1 m,

L1 = 10*log(I1/I0)

Let, at distance 'r',

L2 = 10*log(I2/I0) = L1/2

So, L1 - L2 = L1/2

10*log(I1/I0) - 10*log(I2/I0) = 5*log(I1/I0)

10*log(I1/I2) = 5*log(I1/I0)

10*log(I1) - 10*log(I2) = 5*log(I1) - 5*log(I0)

5*log(I1) - 10*log(I2) = 60

5*log(I1/I2^2) = 60

log(I1/I2^2) = 12

I1/I2^2 = 10^12

here, I1 = P/(4*pi*r1^2)

I2 = P/(4*pi*r2^2)

then,

(r2^2/r1)^2 = 10^12

r2^2/r1 = 10^6

given, r1 = 1 m

then,

r2^2 = 10^6

r2 = sqrt(10^6)

r2 = 1000 m

So, correct option is B.

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