First slide

Characterstics of wave

Question

A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength $2 π m$ and frequency of $\frac{1}{π} H z$ is represented by

Moderate

A

$y = \sin (10 π x - 20 π t)$
B

$y = \sin (2 π x + 2 π t)$
C

$y = \sin (x - 2 t)$
D

$y = \sin (2 π x - 2 π t)$

Solution

The standard equation of a wave travelling along +ve x-direction is given by
$y = A \sin (k x - ω t)$
Where A = Amplitude of the wave
k = angular wave number
$ω$ = angular frequency of the wave
$G i v e n : A = 1 m, λ = 2 π m, v = \frac{1}{π} H z A s k = \frac{2 π}{λ} = \frac{2 π}{2 π} = 1 ω = 2 π v = 2 π \times \frac{1}{π} = 2 ∴ T h e e q u a t i o n o f t h e g i v e n w a v e i s y = 1 \sin (1 x - 2 t) = \sin (x - 2 t)$

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