Question

The sound level in decibels is typically expressed as β = 10 log (I/I0), but since sound is a pressure wave, the sound level can be expressed in terms of a pressure difference. Intensity depends on the amplitude squared, so the expression is β = 20 log (P/P0), where P0 is the smallest pressure difference noticeable by the ear: P0 = 2.00·10-5 Pa. A hair dryer has a sound level of 79 dB, find the amplitude of the pressure wave generated by this hair dryer

Answer 1

20Log(P/Po) = 79db,
Divide both sides by 20:
Log(P/Po) = 3.95,
P/Po = 10^3.95,
Multiply both sides by Po:
P = 10^3.95 * Po,
P = 1*10^3.95 * 2*10^-5,
P = 2*10^-1.05 = 0.1783.