If a sound intensity level of 0 dB at 1000 Hz corresponds to a maximum gauge pressure (sound amplitude) of 10–9 atm , what is the maximum gauge pressure in a 60-dB sound? What is the maximum gauge pressure in a 120-dB sound?

Solution 25PE

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

(dB) =

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

Calculate the ratio of intensity of sound from relation,

(dB) - (dB) = 60

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

Substitute forand forin equation,

(dB) - (dB) = 60

Substitute for(dB) and for (dB),

- = 60

= 60

=

Hence, the sound istimes more intense.

As intensity is directly proportional to square of its amplitude thus,

Here is the amplitude.

Therefore,

=

Substitutefor,

=

Square root both side and get,

= 1000

= 1000

Substitute for

= (1000) ()

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