First slide

Travelling wave

Question

When a wave travels in a medium the displacements of particles are given by $y = 0.01 \sin [2 π (2 t - 0.01 x)]$ where $x, y$ are in meter and $t$ in seconds. Find wavelength, wave velocity.

Moderate

A

100 m, 200 m/sec
B

300 m, 400 m/sec
C

200 m, 500 m/sec
D

zero, 300 m/sec

Solution

$T h e g i v e n e q u a t i o n i s y = 0.01 \sin (4 π t - 0.01 \times 2 π x) C o m p a r i n g t h i s e q u a t i o n w i t h y = A \sin (w t - k x) w e g e t, A m p l i t u d e A = 0.01 m F r e q u e n c y w = 4 π r a d / s \Rightarrow 2 π n = 4 π \Rightarrow n = 2 H z W a v e l e n g t h \begin{array}{l} k = 0.01 \times 2 π \\ \Rightarrow 2 π / λ = 2 π / 100 \\ λ = 100 m \\ W a v e S p e e d \\ ∴ v = n λ = 2 \times 100 = 200 m / s \end{array}$

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