A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the phase at S₁ and S₂ is zero at this instant, and the waves shown arriving at P₂ both arrive with amplitude A, the difference in phase angle at point P₂ (in radians) is A) 0. B) π/2. C) π. D) 3π/2. E) 2π.

Question

Quizplus · Accepted Answer

At point P₂, the distance to source S₁ is $r_1=\frac{3\lambda}{2}$ and the distance to source S₂ is $r_2=\frac{2\lambda}{2}=\lambda$. Let's assume that the wavelength of the waves is $\lambda$. The phase difference between the two waves at point P₂ can be calculated as follows: $\Delta\Phi=2\pi\frac{r_2-r_1}{\lambda}=2\pi\frac{\lambda}{2\lambda}=2\pi\frac{1}{2}=\pi$ Therefore, the phase difference at point P₂ is $\pi$ or choice C.

A Planar Cross Section Through Two Spherical Waves Emanating from the Sources