The figure shows two point sources S 1 and S 2 that emit sound of wavelength ? =

Question

The figure shows two point sources S1 and S2 that emit sound of wavelength ? = 1.12 m. The emissions are isotropic and in phase, and the separation between the sources is d = 18.0 m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. Start with P very far away (x=infin). As you then move P in along the x axis toward the origin, at what coordinate x does the second minimum occur?

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The figure shows two point sources S1 and S2 that emit sound of wavelength ? = 1.12 m. The emissions are isotropic and in phase, and the separation between the sources is d = 18.0 m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. Start with P very far away (x=infin). As you then move P in along the x axis toward the origin, at what coordinate x does the second minimum occur? just give the right answer and get 5 star rating

Explanation / Answer

a) call d1 the distance from S1 to the point and d2 the distance from S2

the difference in distance, d2 - d1 = Sqrt[18+x^2] -x

as x gets large, this difference approaches zero, so that when x-> infinity, the waves are in phase and interfere constructively

c) since the phase difference is zero at x-> infinity, the phase difference will increase as you first move toward S1, but will oscillate

d) the difference in distance is Sqrt[18^2+x^2]-x

this will equal 0.5L = 1m when

Sqrt[18^2+x^2]-x = 1

or Sqrt[18^2+x^2]=1+x

square both sides

18^2+x^2 = 1+2x +x^2

x=161.5 m

for a phase difference of 1.12m, follow the same procedure

d2-d1 = Sqrt[324+x^2] - x =1.12

324+X^2 = x^2+2.24x+1.2544

x = 144.08

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