Question

A sinusoidal wave has an amplitude of 2cm. It is travelling in the negative x-direction. The distance between two crests is 2cm. The angular frequency is πs^-1. What is the displacement of the particle at x = 20.5cm, at t = 10s? Assume that at t=0 & x=0 the particle was at the mean position and going downwards. ‘x’ &’y’ are in cm.

(a) 0cm

(b) 1cm

(c) -1cm

(d) -2cm

The question was posed to me in quiz.

The doubt is from Displacement Relation in a Progressive Wave topic in section Waves of Physics – Class 11

Answer 1

Right choice is (d) -2cm

Easy explanation: The equation suiting the given conditions will be: y = Asin(kx+wt+a)

At x=0, t=0, velocity is negative, so ‘a’ will be π.

k = 2π/λ = π.

∴ y = 2sin(πx + 2t + π).

At x=20cm & t=10s,

y = 2sin(20.5π + 10π + π)

= 2sin(31.5π)

= -2cm.