Question

A wave y=asin(ωt-kx), on a string meets with another wave producing a node at x = 0. Then, the equation of the unknown wave is?

(a) y=asin⁡(ωt+kx)

(b) y=-asin⁡(ωt+kx)

(c) y=asin⁡(ωt-kx)

(d) y=-asin⁡(ωt-kx)

This question was addressed to me during an interview for a job.

Question is from Longitudinal Waves topic in section Waves of Engineering Physics I

Answer 1

Correct answer is (b) y=-asin⁡(ωt+kx)

Explanation: For producing node, the superposing wave must travel in the opposite direction (x term must have opposite sign) and its displacement must be negative. Hence the correct option is y=-asin⁡(ωt+kx)

Moreover,

y=y1+y2=asin⁡(ωt-kx)-asin⁡(ωt+kx)

y=-2acosωtsinkx

At x=0, y = 0. That is a node is formed.