The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?

Solution 24PE

Sound intensity level in units of decibels (dB) can be written as,

(dB) =

Here, is the sound intensity level, is the intensity of sound andis the threshold intensity of hearing.

Calculate the ratio of intensity of sound from relation,

(dB) - = 40

Here, is the initial sound intensity level and is the final sound intensity level.

Substituteforandforin equation,

(dB) -

Substitute for (dB) and for (dB),