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A transverse harmonic wave on a string is given by $$y(x, t) = 5\sin6t + 0.003x$$ where $$x$$ and $$y$$ are in cm and $$t$$ in sec. The wave velocity is _______ m s$$^{-1}$$.
Correct Answer: 20
Given wave equation
$$y(x,t)=5\sin(6t+0.003x)$$
Compare with standard form
$$y=A\sin(\omega t\pm kx)$$
So
$$\omega=6\ \text{rad/s}$$
and
$$k=0.003\ \text{cm}^{-1}$$
Wave speed is
$$v=\frac{\omega}{k}$$
$$=\frac{6}{0.003}$$
$$=2000\text{ cm/s}$$
Convert to m/s:
$$2000\ \text{cm/s}=20\ \text{m/s}$$
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