Question

Your roommate has decided to scare your cat. the cat is sleeping 1.9 m away from the stereo when your roommate turns it on. At 1.9 m the loudness of the music is beta = 126.7 dB.

1) What is the intensity of the music at your cat?

a) I cat = 0.94 W/m^2 b) I cat = 4.7 W/m^2 c) I cat = 12 W/m^2

2) What is the intensity of the music half way between the cat and the stereo?

a) I half = I cat / 4 b) I half = 4 I cat c) I half = I cat / 2

3) The cat wakes up and runs across the room to get away from the noise. How far must your cat run from his current position to experience the music at I quiet = I cat / 20 W/m^2?

a) 8.5 m b) 38 m c) 6.6 m

Answer 1

Part A.

Sound level is given by:

SL = 10*log (I/I0)

I0 = Threshold intensity = 10^-12 W/m^2

SL = 126.7 dB

Using above values:

log (I/I0) = SL/10

I = I0*10^(SL/10)

I = 10^-12*10^(126.7/10)

I = 4.677 W/m^2 = 4.7 W/m^2

Correct option is B.

2.

At the distance halfway between the cat and stereo intensity will be

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

Since power of sound (stereo) is constant, So intensity is inversely proportional to the square of distance from power source

I2/I1 = (r1/r2)^2

I2 = I1*(r1/r2)^2

r2 = r1/2, So

r1/r2 = 2

I2 = 4.7*(2)^2 = 4*4.7

I2 = 4*I_cat

Correct option is B.

3.

for cat to experience quiet music,

I_quiet = I_cat/20 = 4.7/20 = 0.235 W/m^2

Now

I_quiet/I_cat = (r1/r2)^2

r1 = 1.9 m

r2 = distance at which music will be quiet = ?

r2 = r1*sqrt (I_cat/I_quiet)

r2 = 1.9*sqrt (4.7/0.235) = 8.497 m

r2 = 8.5 m

Correct option is A.

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