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A transverse wave propagating along x-axis is represented by
$y(x, t) = 8.0\sin\left(0.5\pi x - 4\pi t - \dfrac{\pi}{4}\right)$
where $x$ is in metres and $t$ is in seconds. The speed of the wave is :-
$y(x, t) = 8.0\sin\left(0.5\pi x - 4\pi t - \dfrac{\pi}{4}\right)$
where $x$ is in metres and $t$ is in seconds. The speed of the wave is :-
A
$4\pi$ m/s
B
$0.5\pi$ m/s
C
$\dfrac{\pi}{4}$ m/s
D
8 m/s
Detailed Solution
Compare with the standard equation $y = A\sin(kx - \omega t + \phi)$.
Wave number: $k = 0.5\pi$ rad/m
Angular frequency: $\omega = 4\pi$ rad/s
Speed of the wave: $v = \dfrac{\omega}{k}$
$v = \dfrac{4\pi}{0.5\pi}$
$v = 8$ m s$^{-1}$
Wave number: $k = 0.5\pi$ rad/m
Angular frequency: $\omega = 4\pi$ rad/s
Speed of the wave: $v = \dfrac{\omega}{k}$
$v = \dfrac{4\pi}{0.5\pi}$
$v = 8$ m s$^{-1}$