Question

Which of the following equations represents a travelling wave ?

• A. $y = Ae^{k\cos(\omega t - \theta)}$
• B. $y = Ae^{-x^2} (vt + \theta)$
• C. $y = A\sin(15x - 2t)$
• D. $y = A\sin x \cos \omega t$

Hint:

For a function to represent a wave, it must satisfy the wave equation $\frac{\partial^2 y}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 y}{\partial t^2}$.

Answer 1

The Correct Option is C

Step 1: A travelling wave must be of the form $y = f(ax \pm bt)$.
Step 2: Option (C) $y = A\sin(15x - 2t)$ fits this form perfectly.
Step 3: Option (D) represents a stationary (standing) wave because the space and time variables are in separate trigonometric functions.