A person stands directly in front of two speakers that are emitting the same pure tone.

Question

The person then moves to one side until no sound is heard. At that point, the person is 4.90 m from one of the speakers and 4.93 m from the other. What is the frequency (in Hz) of the tone being emitted? (Assume air temperature to be 20°C.)

I believe it is 5500 hz

Answer 1

You are close.

The thing to remember is that we are assuming the speakers are interfering constructively at the beginning. Constructive interference of two wavelengths occurs if the two waves are within integer wavelengths of each other, while destructive interference occurs at half-integer wavelengths. The point at which we stop hearing the sound is when we encounter the first half-integer wavelength difference.

In this case, it is at .03 m, or the change in distance, which implies the wavelength emitted is .06 m. Since the speed of air at that temp. is 343 m/s, then the answer comes out to 343/.06, or roughly 5716 Hz.