The figure shows two point sources S1 and S2 that emit sound of wavelength ? = 1

Question

The figure shows two point sources S1 and S2 that emit sound of wavelength ? = 1.63 m. The emissions are isotropic and in phase, and the separation between the sources is d = 14.2 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?

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[16+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[16^2+x^2]-x this will equal 0.5L = 1m when Sqrt[16^2+x^2]-x = 1 or Sqrt[16^2+x^2]=1+x square both sides 16^2+x^2 = 1+2x +x^2 x=127.5 m for a phase difference of 2m, follow the same procedure d2-d1 = Sqrt[256+x^2] - x =2 256+X^2 = x^2+4x+4 x = 63m similarly for a phase difference of 3 m: 256+x^2 = x^2+6x+9 x=41.167m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.