all of these points

Question

A quiet whisper is measured at 30 dB and a loud shout at 110 dB. (Aear canal = 1.54×10−4 m2, Zair = 413 kgm−2 s−1)

(a) What power, in watts, is delivered to the opening of the ear canal during the whisper?

(b) How many times larger is the power (in watts) delivered to the ear canal by the shout?

(c) What is the pressure variation during the whisper?

(d) How many times larger is the pressure variation during the shout?

Answer 1

a)      In terms of pressure , a 30 dB sound level means

30 = 20 log( p/p0)   where p0 = 20 microP

So p = 632 microP  632 micro Pascal

A formula for the power delivered by a sound wave is P = p^2 A / z

Where z is the specific impedance of air,  z = 413 kg /s/ m^2

Putting this together with A = 1.54E-4  gives

P = 1.49E-9 W

b)     Every increase of 10 dB means a factor of 10 in power,

 (110-30 )/10 = 8  so the power is larger by a factor of 10^8

c)      632 mircoP  as above

d)     Since the power is proportional to p^2,  the pressure is greater by a factor of 10^4 in the shout compared with the whisper.