The fringe equations only apply when the observations are made far away from poi

Question

The fringe equations only apply when the observations are made far away from point sources (and so they do not apply here). This problem tests your understanding of the relationship between interference and path length differences. Two loudspeakers, separated by a distance 5.70 m, are playing the same frequency. Initially you are standing in front of the speakers, equidistant from them, and 13.60 m from the line connecting them. You hear a sound of maximum intensity. As you walk parallel to the line connecting the speakers, maintaining your distance of 13.60 m, you first hear a minimum of sound intensity when you are directly in front of one of the two speakers. Find the frequency of the sound. Assume 343 m/s as the speed of sound.

Explanation / Answer

let lamda is the wavelength of the sound wave.

when the you are infront of one of the speakers,

the path defference of the two sound waves reached by you,

r2 - r1 = lamda/2 (since you are listening minima)

r2 - r1 = lamda/2

sqrt(13.6^2 + 5.7^2) - 13.6 = lamda/2

1.146 m = lamda/2

==> lamda = 2*1.146

= 2.292 m

now use,

v = lamda*f

==> f = v/lamda

= 343/2.292

= 150 Hz <<<<<<<<----------------Answer

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