Solutions to problems on Loudness

Rossing 6.4 Let the quiet sound have the level, L1 and amplitude p1.
Let the loud sound have the level, L2=L1 + 46 dB and amplitude p2. Then,

L2 - L1=20 log(p2/p0) - 20log(p1/p0), using the definition of sound level
Using a rule for logarithms, this can be written as
L2 - L1=20 log(p2/p1)
so, 46dB = 20 log(p2/p1), or
102.3 = 200 = p2/p1

Rossing 6.9

50 dB = 20 log(p/p0), or
102.5 = p/p0, or
p = (316) x (2 x 10-5 N/m2) = 6.3 x 10-3N/m2

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Last updated: 18 Oct 1999
Comments: bland@indiana.edu