Question

Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 276 Hz sound that is in phase. An observer at the center of the gym experiences constructive interference.

Part A

How far toward either speaker must the observer walk to first experience destructive interference?

Answer 1

Here, frequency , f = 276 Hz

=> wavelength = 343/276

                          = 1.242 m

Thus, path difference = (x + d) - ( x - d)

                                    = 2d

For destructive interference

=>   2d =   wavelength/2

=> d = wavelength/4

         = 1.242/4

         = 0.3105 m

Thus, far toward either speaker must the observer walk   =   0.3105 m