Examples of working with logarithmic functions
All work with the definition of dB:
dB = 20log
10
(P/P
ref
).
SPL = 20log
10
(P/P
ref
), where P
ref
= 20 micropascals (20
μ
Pa)
And the basic knowledge that if 10
x
= y, then log
10
(y) = x .
Telephone problem (absolute SPL calculations)
1) The amplitude of the sound pressure wave generated by a particular telephone ringing is 0.2
Pa. What is the sound pressure level?
Given an sound intensity, P, calculate the SPL (relative to the standard reference, 20 uPa).
SPL (dB) = 20log
10
(P/P
ref
) = 20log
10
(0.2/0.00002) = 20log
10
(10,000) = 20*4 =
80 dB
2) The sound pressure level of a telephone ringing is 80 dB. What is the physical amplitude of
the sound wave?
Given a SPL, calculate the amplitude of the sound pressure wave.
.
SPL (dB) = 20log
10
(P/P
ref
) => 80 = 20log
10
(P/0.00002) => 4 = log
10
(P/0.00002) =>
4 = log
10
(P/0.00002) => 10
4
= P/0.00002 => P = 0.00002 x 10
4
=
0.2 Pa
Earplug problem (relative SPL)
. Using these two facts, answer the following questions:
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 Spring '08
 OLMAN
 UPA, SPL, 0.02 pa, 0.2 pa, 0.002 Pa

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