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# If a sound intensity level of 0 dB at 1000 Hz corresponds ## Problem 25PE Chapter 17

College Physics by Urone | 1st Edition

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Problem 25PE

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?

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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  for and  for in equation, (dB) - (dB) = 60

Substitute  for (dB) and  for (dB),  -  = 60  = 60 = Hence, the sound is times more intense.

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

Therefore, =  Substitute for , =  Square root both side and get, = 1000 = 1000 Substitute for  = (1000) ( )

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##### ISBN: 9781938168000

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