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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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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?

Step-by-Step Solution:
Step 1 of 3

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) ()

...

Step 2 of 3

Step 3 of 3

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