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A wave travelling in positive X-direction with A = 0.2 m, velocity = 360 m/s and λ = 60 m, then correct expression for the wave is : -
A
$y = 0.2\sin\left[2\pi\left(6t + \dfrac{x}{60}\right)\right]$
B
$y = 0.2\sin\left[\pi\left(6t + \dfrac{x}{60}\right)\right]$
C
$y = 0.2\sin\left[2\pi\left(6t - \dfrac{x}{60}\right)\right]$
D
$y = 0.2\sin\left[\pi\left(6t - \dfrac{x}{60}\right)\right]$
Detailed Solution
For a wave travelling in the positive x direction: $y = A\sin\left[2\pi\left(\dfrac{t}{T} - \dfrac{x}{\lambda}\right)\right] = A\sin\left[2\pi\left(\nu t - \dfrac{x}{\lambda}\right)\right]$
Frequency: $\nu = \dfrac{v}{\lambda} = \dfrac{360}{60} = 6$ Hz
$A = 0.2$ m, $\lambda = 60$ m
$y = 0.2\sin\left[2\pi\left(6t - \dfrac{x}{60}\right)\right]$
(The plus sign would describe a wave travelling in the negative x direction.)
Frequency: $\nu = \dfrac{v}{\lambda} = \dfrac{360}{60} = 6$ Hz
$A = 0.2$ m, $\lambda = 60$ m
$y = 0.2\sin\left[2\pi\left(6t - \dfrac{x}{60}\right)\right]$
(The plus sign would describe a wave travelling in the negative x direction.)