Question

The equation of a transverse wave travelling along a string is \( y(x, t) = 4.0 \sin \left( 20 \times 10^{-3} x + 600t \right) \) mm, where \( x \) is in mm and \( t \) is in seconds. The velocity of the wave is:

• A. +30 m/s
• B. -60 m/s
• C. -30 m/s
• D. +60 m/s

Hint:

The velocity of a wave is calculated using the relation \( v = \frac{\omega}{k} \), where \( \omega \) is the angular frequency and \( k \) is the wave number.

Answer 1

The Correct Option is C

The general equation for a wave is given by: \[ y(x, t) = A \sin(kx + \omega t), \] where \( k \) is the wave number and \( \omega \) is the angular frequency. From the given equation, we identify: \[ k = 20 \times 10^{-3} \, \text{m}^{-1}, \quad \omega = 600 \, \text{s}^{-1}. \] The velocity of the wave \( v \) is related to the angular frequency and wave number by: \[ v = \frac{\omega}{k}. \] Substitute the values of \( \omega \) and \( k \): \[ v = \frac{600}{20 \times 10^{-3}} = -30 \, \text{m/s}. \]