A transverse wave propagating along the $x$-axis is represented by: $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \fra

Question

A transverse wave propagating along the $x$-axis is represented by: $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$, where $x$ is in meters and $t$ in seconds. The speed of the wave is:

Accepted Answer

The given wave equation is $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$.
Comparing this with the standard travelling wave equation $y(x,t) = A\sin(kx - \omega t + \phi)$, we get:
Angular wave number, $k = 0.5\pi 	ext{ rad/m}$
Angular frequency, $\omega = 4\pi 	ext{ rad/s}$
The speed of the wave $v$ is given by the formula:
$v = \frac{\omega}{k}$
$v = \frac{4\pi}{0.5\pi} = 8 	ext{ m/s}$.

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