The sound of a band is rated as 60 dB at a distance of 10.0 m. What is the sound intensity level of the band when one is 20.0 m from the band?
A) 56 dB
B) 54 dB
C) 52 dB
D) 50 dB
E) 48 dB

Question

Quizplus · Accepted Answer

The sound intensity level (SIL) is given by:

SIL = 10 log(I/Io) where I is the sound intensity and Io is the reference intensity of 1.0 x 10^-12 W/m^2.

From the problem, we know that SIL1 = 60 dB when the distance is 10.0 m. We can use the inverse square law for sound to find the sound intensity at a distance of 20.0 m:

I2/I1 = (r1/r2)^2

I2/I1 = (10.0 m/20.0 m)^2

I2/I1 = 0.25

I2 = 0.25 I1

Now we can find the new SIL:

SIL2 = 10 log(I2/Io)

SIL2 = 10 log(0.25) + 10 log(I1/Io)

SIL2 = -6 dB + SIL1

SIL2 = 54 dB

Therefore, the answer is B, 54 dB.

The Sound of a Band Is Rated as 60 DB