A handclap on stage in an amphitheater sends out sound waves that scatter from terraces of width `w = 0.75 m` (see figure). The sound returns to the stage as a periodic series of pulses, one from each terrace, the parade of pulses sound like a played note. Assuming that all the rays in Figure are horizontal, find the frequency at which the pulses return (that is, the frequency of the perceived note). Take the speed of sound to be `330m//s`

Explanation

Consider a string of pulses returning to the stage. A pulse that came back just before the previous one has traveled

an extra distance of 2w, taking an extra amount of time `Delta t = 2w//v` .
(a) The frequency of the pulse is therefore
`f = (1)/(Delta t) = (v )/(2w) = (343 m//s)/(2(0.65m)) = 2.6 xx 10^2 Hz`
(b) Since `f prop 1// w` , the frequency would be high if w were smaller.