Question

Two speakers, A and B, have the same power output when on and produce in-phase 69 Hz tones. A listener is 14.3 m from A and 26.8 m from B. When only A is on, the sound level at the listener is 55 dB. The speed of sound is 345 m/s.

A ) What is the intensity at the listener when only A is on?

B) What is the intensity at the listener when only B is on?

C) Show that if both A and B are on, the sound waves are at the listener are out of phase.

D) If the waves are at the listener are out of phase, will the resulting intensity be zero ? Explain.

Answer 1

A] Intensity at A in W/m² is:

B] Since A and B are of same power and the intensity follows the inverse square law, the intensity when only B is on will be:

= 49.54 dB

C]

The path difference between the two is:

and the wavelength of A or B is:

for destructive interference, the path difference should be odd integers of half wavelength.

If the odd integer is selected to be m = 5, then

which is the path difference and so if both A and B are on, the sound waves at the listener will be out of phase.

D] The resultant sound will be minimum but not zero because intensity cannot be added linearly superposition of Electric fields.