Question

A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 2.8×10-3 W/m2. At a distance 1.9 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?

Answer 1

Sound intensity is given by:

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

Since Source of power is constant at both places, So Intensity is inversely proportional to the square of distance.

I2/I1 = (r1/r2)^2

I2 = I1*(r1/r2)^2

r1 = d, and r2 = 1.9*d

So,

I2 = 2.8*10^-3*(d/(1.9*d))^2

I2 = 2.8*10^-3*(1/1.9)^2

I2 = 7.76*10^-4 W/m^2

Part B

Sound Intensity level is given by:

SL = 10*log (I/I0)

I0 = 10^-12 W/m^2 = threshold sound intensity

I = I2 = 7.76*10-4 W/m^2

So,

SL = 10*log (7.76*10^-4/10^-12)

SL = 88.90 dB

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