The loudness of sound decreases as the distance from the source increases. Doubling the distance from a sound multiplies the relative intensity of the sound by one-fourth. When the sound of a speaker is recorded as 80 decibels at 10 feet, what is the decibel reading if four identical speakers are added at 20 feet?
A)83 decibels
B)84 decibels
C)92 decibels
D)93 decibels

Question

Quizplus · Accepted Answer

Doubling the distance from the sound source decreases the intensity to one-fourth. For one speaker, the intensity at 20 feet would be one-fourth of that at 10 feet. Decibels (dB) are calculated on a logarithmic scale. A tenfold increase in intensity adds 10 dB, and a tenfold decrease subtracts 10 dB. Halving the intensity (which is more than a tenfold decrease) subtracts more than 10 dB, but since the intensity is one-fourth, it's effectively halving twice, which would subtract slightly more than 20 dB from the original 80 dB for one speaker. However, adding four identical speakers quadruples the intensity, which compensates for the reduction to one-fourth at double the distance, bringing the intensity back to the equivalent of one speaker at 10 feet, or 80 dB. The combined effect of these changes results in a slight increase in decibels due to the logarithmic nature of the dB scale and the addition of slightly more sound energy from the four speakers being in different locations, leading to a small increase to 83 dB.

The Loudness of Sound Decreases as the Distance from the Source