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 |

**In simple term distance $\lambda$ (one wave length) takes T amount of time.**

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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