Question

You are standing outside with two speakers. The temperature is 0 degrees C. The two speakers are playing sound of the same frequency: a pure sinusoidal sound of the same frequency at the same phase. The speakers are playing at different amplitudes. One speaker is 1.230 meters from you and one is 1.425 meters from you. You hear no sound. Which of the following is a possible frequency of the sound being played?

a. 993 Hz
b. 331 Hz
c. 4965 Hz
d. 1655 Hz
e. 662 Hz

Answer 1

Step-by-step explanation:

No sound is heard , that means there is destructive interference at the place where sound is heard .

Path difference of the source of sound = 1.425 m - 1.230 m

= 0.195 m

Let frequency of sound be n .

wave length = velocity of sound at 0°C / n

λ = 330 / n

for destructive interference ,

path difference = ( 2m+1) λ /2 , where λ is wave length of sound.

0.195 m = ( 2m+1) λ /2

0.195 m = ( 2m+1)330 / 2n

2n = 1692.3 (2m+1)

If m = 0

n = 846 . which is nearest to given frequency of 993 Hz

So 993 Hz is the answer.