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
for
and
for
in 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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