Point A is the midpoint of one of the sides of a square. On the side opposite th

Question

Point A is the midpoint of one of the sides of a square. On the side opposite this spot, two in-phase loudspeakers are located at adjacent corners, as in Figure 27.39. Standing at point A you hear a loud sound because of constructive interference between the identical sound waves coming from the speakers. As you walk along the side of the square toward either empty corner, the loudness diminishes gradually to nothing and then increases again until you hear a maximally loud sound at the corner. If the length of each side of the square is 4.7 m, find the wavelength of the sound waves.

Explanation / Answer

Using basic principles .. the first maximals (beyond the central one) heard at each corner are due to the waves from each speaker having a path difference of 1 to these points.(given that the speakers transmit inphase).
so ..( the diagonal of the square layout) - (the side length of the square) = 1

by Pythagoras .. (diagonal)² = 2(4.7²) .... diagonal = 6.64 m

and path difference (1) = 6.64 - 4.7 .=1 = 1.94 m

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