Question

A wave travelling in a stretched string is described by the equation \( y = A\sin(kx - \omega t) \). The maximum particle velocity is :

• A. \(A\omega\)
• B. \( \omega/k \)
• C. \( d\omega/dk \)
• D. \( x/t \)

Hint:

Maximum particle velocity in wave motion is \(A\omega\), not wave speed.

Answer 1

The Correct Option is A

Concept: Particle velocity: \[ v = \frac{\partial y}{\partial t} \]

Step 1: Differentiate.
\[ v = -A\omega \cos(kx - \omega t) \]

Step 2: Maximum value.
\[ v_{max} = A\omega \]