Question

An equation of a wave is given by: y = 2sin(3x-2t+π/2). What is the minimum distance between two points having the same phase?

(a) 3

(b) π/2

(c) 2π/3

(d) π

The question was asked in examination.

Origin of the question is Displacement Relation in a Progressive Wave in chapter Waves of Physics – Class 11

Answer 1

The correct answer is (c) 2π/3

Best explanation: In the given equation the phase is 3x-2t+π/2.

This is repeated after every 2π.

∴ sin( 3x-2t+π/2) +2nπ = sin( 3x-2t+π/2).                                                                                                                                          We can consider the case at t=0, sin(3x+π/2) = sin(3x+π/2+2nπ)                                                                                    OR cos(3x) = cos(3x+2nπ)                                                                                                                                                   ∴ n = 1 for minimum difference.                                                                                                                                                    Minimum distance can be found from kx = 2π                                                                                                                OR x = 2π/k = 2π/3.