Problem 23PE

Ten cars in a circle at a boom box competition produce a 120-dB sound intensity level at the center of the circle. What is the average sound intensity level produced there by each stereo, assuming interference effects can be neglected?

Solution 23PE

If a source is emitting sound of some intensity then n number of sources emitting sound of same intensity will definitely cause increase in sound intensity and intensity emitted by identical sources will be times of the single source if interference is not considered.

The expression to find the intensity level of sound produced by 10 cars is,

= (10 d)

Substitute, 120 dB for and for in the expression of intensity level of sound,

120 dB = (10 dB) ()

= ()

Further solve,

= 1 w/

Hence the intensity of sound for stereo of 10 cars is 1 w/.

The expression to find the intensity of 10 stereo is,

= (10)

Rearrange the expression for intensity of single car.

Substitute 1 w/ for in the above expression.

=

= w/

The expression to find the sound intensity level for each car stereo is,

= (10 dB)

Substitute, w/ for and w/ for in the expression of intensity level of sound,

= (10 dB)

= (10 dB) 11

= 110 dB

Hence each stereo of car contributes to 110 dB of sound at the boom box competition.