First slide

Travelling wave

Question

The equation of a wave travelling on a string is $y = 4 \sin \frac{π}{2} (8 t - \frac{x}{8})$ . If x and y are in cm, then velocity of wave is

Easy

A

64 cm/sec in – x direction
B

32 cm/sec in – x direction
C

32 cm/sec in + x direction
D

64 cm/sec in + x direction

Solution

The given equation can be written as $y = 4 \sin (4 πt - \frac{πx}{16}) \Rightarrow (v) = \frac{Co-efficient of t (ω)}{Co-efficient of x (K)}$
$\Rightarrow v = \frac{4 π}{π / 16} = 64 cm / \sec$ along +x direction.

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