Problem # 23: Two point sources S 1 and S 2 that emitsound of wavelength = 2.00

Question

Problem # 23: Two point sources S1 and S2 that emitsound of wavelength = 2.00 m. The emissions are isotropicand in phase, and the separation between the sources is d = 16.0 m.In the fig., S1 is at the origin and S2 isnegative y- axis. At any point P on the x axis, the wave fromS1 and the wave from S2 interfere. When P isvery far away (x ˜ ), what are (a) the phasedifference between the arriving waves from S1 andS2 and (b) the type of interference they produce? Nowmove the point P along the x axis toward S1. (c) Doesthe phase difference between the waves increase or decrease? Atwhat distance x do the waves have a phase difference of (d)0.50, (e) 1.00, and (f) 1.50? Problem # 23: Two point sources S1 and S2 that emitsound of wavelength = 2.00 m. The emissions are isotropicand in phase, and the separation between the sources is d = 16.0 m.In the fig., S1 is at the origin and S2 isnegative y- axis. At any point P on the x axis, the wave fromS1 and the wave from S2 interfere. When P isvery far away (x ˜ ), what are (a) the phasedifference between the arriving waves from S1 andS2 and (b) the type of interference they produce? Nowmove the point P along the x axis toward S1. (c) Doesthe phase difference between the waves increase or decrease? Atwhat distance x do the waves have a phase difference of (d)0.50, (e) 1.00, and (f) 1.50?

Explanation / Answer

(a)the phase difference between the arriving waves fromS1 and S2 = (2/) * = (2/) * d *sin sin = (y/d) y = L(m/d),m = 0,1,2,3............. (b)they produce constructive interference because theemissions are isotropic and in phase. (c)the phase difference between the waves decreases,this isbecause L decreases when we move point P along the x axis towardS1. (d)the phase difference is = (2/) * or = (/2) * Here, = 0.50,1.00 and 1.50

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