Question

A 100Hz tone at 40 phons is played simulataneously with a 1000 Hz tone at 60 phons. What is the to intensity of the combined sound ?

A) 40 dB

B) 60 dB

C) 64 dB

D) 100 dB

E) 120 dB

Answer 1

Here, we have two sound waves

a) 40 phons @ 100Hz

b) 60 phons @ 1000Hz

Both sound waves are played simultaneously meaning they will interfere constructively.

Now, lets get the Intensities of these waves in decibels,

40 phons @ 100 Hz corresponds to 60 dB.

To get this 60 dB values please see the attached Graph for your reference.

And by the definition of phons,

60 phons @ 1000 Hz = 60 dB

Now lets add up the two intensities (since they are constructive)

Resultant Intensity = 60 dB + 60 dB

Also, Intensity (in dB) = 10 log(I/Io)

60 = 10 log(I/Io)

log(I/Io) = 6

I = Io x 10⁶

I = 10^-12 x 10⁶

I = 10^-6

^Now,

Total Intensity = 2 x I

Total Intensity = 2 x 10^-6

Intensity in dB = 10log (2*10^-6/10^-12)

Intensity in dB = 10*(log(2)+6)

Intensity in dB = 10*(0.3010+6)

Intensity in dB = 63

So the answer is approximately 64 dB i.e Option C