Question

A small loudspeaker is located at a large distance to the east from you. The loudspeaker is driven by a sinusoidal current whose frequency can be varied. Estimate the lowest frequency for which your ears would receive the sound waves exactly out of phase when you are facing north. (Assume that the speaker and your ears are on the same line and let the distance between your ears be about 18 cm. Take the speed of sound in air to be 343 m/s.)

answer in (kHz)

Answer 1

If your ears receive the sound exactly out of phase, the waves arriving at your ear that is farthest from the speaker must be traveling onehalf wavelength farther than the waves arriving at your ear that is nearest the speaker. The lowest frequency corresponds to the longest wavelength. Assume that the speaker and your ears are on the same line and let the distance between your ears be about 18 cm. Take the speed of sound in air to be 343 m/s

the frequency receive by your ear is given by f = v/

let dr be the distnace between your ear(the path difference) to obtain dr = (1/2)

or, = 2 dr

so f = v/ 2 dr = (343 m/s) / 2x(18x10^-2 m) = 0.95 kHz

so betwen 0.90 kHz to 1 kHz