Let's consider the following wave motion,
Image Courtesy: isvr.soton.ac.uk/span> |
Position-Displacement plots |
We also know that this propagation is due to the oscillation of the water molecule (as shown in the red dot in the above animation) at any given point. During this propagation the water molecule completes a one complete oscillation (up and down), that is time taken for one complete wave propagation to take place and is equal to the time taken for one complete oscillation of the water molecules $(T)$. The plot of the displacement-time for oscillation is given below,
Displacement-Time plot |
So since,
\begin{align*}
v&=\frac{distance}{time}=\frac{\lambda}{T} \\&=\lambda f \end{align*}
Thus, the speed of wave propagation is given by,
$$v=\lambda f$$
Here's a demonstration video,
$Ex.$ Given a sound wave of frequency $400Hz$ and wave length of $0.8m$. Calculate the speed of the propagating sound wave.(ans:$320ms^{-1}$)
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