Question

Two point sources of sound are kept at a separation of 10 cm. They vibrate in phase to produce waves of wavelength 5.0 cm. What would be the phase difference between the two waves arriving at a point 20 cm from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources?

Answer 1

Given:
Separation between the two point sources ∆x = 10 cm
Wavelength λ = 5.0 cm

(a)
$$\begin{gathered} \mathrm{Phase}\mathrm{difference}\mathrm{is}\mathrm{given}\mathrm{by}: \\ \varphi =\frac{2\mathrm{\pi }}{\lambda }∆x \\ So, \\ \varphi =\frac{2\mathrm{\pi }}{5}\times 10=4\mathrm{\pi } \end{gathered}$$

Therefore, the phase difference is zero.

(b) Zero: the particles are in the same phase since they have the same path.