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

$$y=A\sin(\omega t\pm kx)$$

$$\omega=6\ \text{rad/s}$$

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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