First slide

Speed of wave

Question

The displacement of a particle in a medium can be expressed as
$y = 10^{- 6} \sin (100 t + 20 x + π / 4) metre,$ where t is in second and x in meter. The speed of the wave is

Moderate

A

2000m/s
B

5 m/s
C

20 m/s
D

$5 π m / s$

Solution

Given that
$y = 10^{- 6} s i n (100 t + 20 x + π / 4) T h e s t a n d a r d e q u a t i o n i s y = a s i n \frac{2 π}{λ} (v t - x + ϕ) C o m p a r i n g t h e s e t w o e q u a t i o t r s, w e \frac{2 π V}{λ} = 100 and \frac{2 π}{λ} = 20 20 v = 100 or v = 5 m / s$

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