Question

Two people hear a tornado siren, but one listener is 81.9 times farther away from the source of the sound than the other. What is the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener

Answer 1

-38.26dB is the intensity level of the sound for the more distant listener relative to that for the nearer listener

By using the inverse square law,

As one listener is 81.9 times farther away from the source of the sound than the other.

Then Increasing the distance by 81.9 times reduces the intensity by

$81.9^{2}$ = 6707.61 times

The intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is:

= 10log(ratio of intensities)

= 10log(1/6707.61)

= 10log(0.000149)

=10 × -3.826

= -38.26dB (The negative sign represents the sound is less intense for the farther listener)

So, the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is -38.26dB

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