Question

The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are ____________

(a) coskxsinωt

(b) k^2 ω^2-ω^2 t^2

(c) cos^2 (kx+ωt)

(d) cos^2 (k^2 x^2-ω^2 t^2)

The question was asked during an interview.

Enquiry is from Transverse Waves in division Waves of Engineering Physics I

Answer 1

Right answer is (a) coskxsinωt

Easiest explanation: y= coskxsinωt is the only equation of standing wave. The conditions for a function of x and t to represent a wave is

(∂^2 y)/∂x^2 = constant×(∂^2 y)/∂t^2

Only first expression satisfies this condition.