A loudspeaker at the front of a room and an identical loudspeaker at the rear of

Question

A loudspeaker at the front of a room and an identical loudspeaker at the rear of the room are being driven by the same oscillator at 460 Hz. A student walks at a uniform rate of 0.90 m/s along the length of the room. She hears a single tone repeatedly becoming louder and softer.
(a) Consider these variations as beats between the Doppler-shifted sounds the student receives. Calculate the number of beats the student hears per second. ___Hz
(b) Consider the two speakers as producing a standing wave in the room and the student as walking between the antinodes. Calculate the number of intensity maxima the student hears each second. ____Hz will rate!

Explanation / Answer

The path length difference to the point ?x = sqrt(6.15^2+1.85^2) - 6.15. The wavelength ? = c/f. The phase shift in radians is 2*pi*?x/?. A couple of nits: Phase difference is not directional, it's a condition at a point, so I don't know what "perpendicular to the plane of the speakers" is about. And anyway two points (e.g., two speaker locations) don't determine a plane.

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