Question

A travelling wave in a medium is given by the equation \(y=a\sin(\omega t-kx)\). The maximum acceleration of the particle in the medium is

• A. \(\omega\)
• B. \(a\omega^2\)
• C. \(\dfrac{\omega}{k}\)
• D. \(\dfrac{x}{k}\)
• E. \(ak\)

Hint:

In SHM or wave-particle motion: \[ a_{\max}=\omega^2 A \] where \(A\) is amplitude.

Answer 1

The Correct Option is B

For the wave: \[ y=a\sin(\omega t-kx) \] Particle acceleration is: \[ \frac{\partial^2 y}{\partial t^2}=-a\omega^2\sin(\omega t-kx) \] Maximum value of acceleration: \[ a_{\max}=a\omega^2 \] Hence, \[ \boxed{(B)\ a\omega^2} \]