Question

(a)

Find the intensity in watts per meter squared of a 200 Hz sound having a loudness of 30 phons.

W/m²

(b)

Find the intensity in watts per meter squared of a 10,000 Hz sound having a loudness of 60 phons.

W/m²

Answer 1

Sound level   

8-10logio Io

Where ${I_0}=10^{-12}\,W/m^2$

logio T10 logo-= 10

1 10103/ 10

120 phon 110 phon 100 phon 90 phon 80 phon 70 phon 60 phon 50 phon 40 phon 30 phon 20 phon 10 phon 0 phon 120 100 80 72 d 60 S45 d O 40 20 -10 40 60100 200 400 800 2000 5000 10,000 50 80 500 1000 4000 8000 Frequency f (Hz)

a)

At frequency
f = 200 H
, with loudness
30 phons
, sound level is
β = 45 dB
( the green lines in the above figure)

Intensity is

-1 010/1010-121045/10 -1075 3.16 10-5 Wm2 In

b)

At frequency
f = 10, 000 H
, with loudness
60 phons
, sound level is
β = 72 dB
( the blue lines in the above figure)

Intensity is

010/1010-121072/10 -10481.58 *10-5W/m2 I1 1.58 10 W/m In