Question

For a home sound system, two small speakers are located so that one is 52 cm closer to the listener than the other. What is the very first frequency of audible sound for these speakers to produce destructive interference at the listener?The speed of sound is 344 m/sec. (1 point)
166 Hz
331 Hz
662 Hz
1323 Hz

Answer 1

You'll get destructive interference if both waves are the same frequency but the peaks of one wave overlap the troughs of the other wave.

That can only happen if one wave has to travel (1/2 wavelength) farther than the other one to reach your ears.  So we want to find the lowest frequency for which 52 cm is 1/2 of a wavelength ... the wavelength is 104 cm.

Frequency = (speed) / (wavelength)

Frequency = (344 m/s) / (104 cm)

Frequency = (344 m/s) / (1.04 meter)

Frequency = (344 / 1.04) per second

Frequency = 330.8 Hz .