Two tuning forks are struck simultaneously. Fork A vibrates at 256 Hz, and fork B vibrates at 260 Hz. The sound waves from the forks superpose in air of uniform properties.
(a) Calculate the beat frequency heard by a listener positioned equidistant from the two forks.
(b) Both forks are carefully retuned so that each frequency increases by 3 Hz. Determine the new beat frequency and compare it with your result from part (a).
(c) Explain why the beat phenomenon arises in terms of the time evolution of the resultant wave amplitude at a fixed point in space.
(d) Without performing explicit trigonometric calculations, sketch one complete time interval over which the listener hears a full beat cycle. Label the points of maximum and minimum sound intensity and indicate their spacing in time relative to the calculated beat frequency.