Question

The mating call of a male cicada is among the loudest noises in the insect world, reaching decibel levels of 105 dB at a distance of 1.00m from the insect. (a) Calculate the corresponding sound intensity. (b) Calculate the sound intensity at a distance of 20.0m from the insect, assuming the sound propagates as a spherical wave. (c) Calculate the decibel level at a distance of 20.0m from 100 male cicadas each producing the same sound intensity.

Answer 1

The sound intensity can be calculated using the formula Intensity = Power / Area. Applying the inverse square law, the sound intensity at a distance of 20.0m can be determined. To calculate the total sound intensity produced by 100 male cicadas, multiply the sound intensity produced by a single male cicada by 100.

Step-by-step explanation:

(a) To calculate the sound intensity, we need to use the formula:

Intensity = Power / Area

We know the sound level is 105 dB, which is equal to 1010.5 times the threshold intensity of 10-12 W/m². So the sound intensity is:

Intensity = 1010.5 * 10-12 W/m²

(b) Using the inverse square law for sound propagation, the sound intensity at a distance of 20.0m is:

Intensity at 20.0m = Intensity at 1.00m / (20.0m)2

(c) If each male cicada produces the same sound intensity, the total sound intensity produced by 100 male cicadas at 20.0m can be calculated by multiplying the sound intensity produced by a single male cicada at 20.0m by 100:

Total sound intensity = Intensity at 20.0m * 100