Question

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10-10. Ahmad, Brandon’s neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10-4. How does Brandon’s sound intensity level compare to Ahmad’s mower?

Brandon’s sound intensity is One-fourth the level of Ahmad’s mower.
Brandon’s sound intensity is One-fourth the level of Ahmad’s mower.
Brandon’s sound intensity is 20 times the level of Ahmad’s mower.
Brandon’s sound intensity is 80 times the level of Ahmad’s mower.

Answer 1

Brandon’s sound intensity is One-fourth the level of Ahmad’s mower

Explanation:

Data

The sound intensity level that Brandon can hear is 10^(-10)

Ahmad’s mower sound intensity level is 10^(-4).

L = 10*log(I/10^(-12))

where L is loudness in decibels and I is sound intensity in watts per square meter.

The loudness that Brandon can hear:

L = 10*log(10^(-10) /10^(-12)) = 10*log(2) = 20

Ahmad’s mower loudness:

L = 10*log(10^(-4) /10^(-12)) = 10*log(8) = 80

One-fourth the level of Ahmad’s mower is 80*(1/4) = 20 which is equal to Brandon’s sound intensity