Discussion
In the given wave equation y=0.05 \(\sin\frac{2\pi}{\lambda}\) (x-200t) m, the velocity of the wave (in ms-1) is
Answer: E
The wave velocity is 200 m s-1.
A travelling wave of the form \(y = A\sin\frac{2\pi}{\lambda}(x - vt)\) moves in the positive x-direction with speed \(v\). Comparing with \(y = 0.05\sin\frac{2\pi}{\lambda}(x - 200t)\) gives \(v = 200\) m s-1 directly.
Equivalently, \(k = \frac{2\pi}{\lambda}\) and \(\omega = \frac{2\pi}{\lambda} \times 200\), so \(v = \frac{\omega}{k} = 200\). The square-root options have no basis in this equation, and 400 doubles the speed.
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