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

1000 m

100 m

2000 m

1,260 m

500 m

Answer 1

Let us convert the sound in W/m^2

Therefore

For 120 db

I1 = (10^12)x(10^-12)

I1 = 1w/m^2

Also when the sound is half loud = 120/2 = 60 db

Therefore

I2 =(10^6)x(10^-12)

I2 = 10^-6 w/m^2

Now we know

Intensity is inversely proportional to square of distance

I ∝ (1/d^2)

Now let

the distance be d1 = 1m for intensity I1

The distance be d2 be for intensity I2

Therefore

I1/I2 = (d2)^2/(d1)^2

1/10^-6 = (d2)^2/ 1^2

10^6 = (d2)^2

d2= 1000m

Therefore

New distance will be 1000 m