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

Answer ⇒ Zero in both the cases.

Explanation ⇒

(a).  Given, distance of one point from the source = 20 m.

Distance of the other point from the same source having 10 cm distance from the one point = 20 + 10 cm.

= 30 cm.

Thus, Path difference(Δx) = 30 - 20

Δx = 10 cm.

Now, the Phase difference is given by the formula,

ΔΦ = 2πΔx/λ

∴ ΔΦ = 2π × 10/5

∴ ΔΦ = 2π × 2

Since Phase difference is an multiple of 2π, hence phase difference is zero.

(b). We know that each point on the perpendicular bisector of a line-segment is equidistant from both ends of the line segment, thus, path difference, Δx=0.

Hence the phase difference =2π× Δx/λ

= 2π*0/λ

= 0 (zero)

Hope it helps.

Answer 2

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.