Question

Define the term wave velocity. Write its SI unit.

Answer 1

Hint : As in the case of any type of velocity, it can be given as the rate of change of displacement with time. It has an SI unit of a typical velocity.

Formula used: In this solution we will be using the following formula;
 $\Rightarrow v = f\lambda $ , where $ v $ is the wave velocity, $ f $ is the frequency of the wave and $ \lambda $ is the wavelength of the wave.

Complete step by step answer
In a propagating wave, there are two velocities that can be said to be possessed. One is by the wave itself, the other is by the particle propagating the wave. These are called the wave velocity and particle velocity respectively.
Wave velocity: this is the velocity in which a wave motion propagates through a medium. Wave motions are generally generated through vibrations. When a part of a medium is vibrated, the particles of the medium set into motion, due to interactive forces these moving particles set other neighbouring particles into motion which also set other particles into motion and on and on. This transfer of motion is the wave motion, and the velocity of propagation is called wave velocity. Since it is a type of velocity, it is measured in meters per second (m/s).
Particle velocity: this is the other type of velocity considered in a wave motion. It is the velocity of the moving particle itself and not the motion caused by the particle. Since, particles are usually in oscillation, their velocity is not constant and changes direction periodically.

Note
Alternatively, through mathematical reasoning, the wave velocity is given by
 $\Rightarrow v = f\lambda $ where $ f $ is the frequency of the wave and $ \lambda $ is the wavelength of the wave.
Now, the SI unit for $ f $ is per second ( $ {s^{ - 1}} $ ), and the SI unit for $ \lambda $ is meters (m). Hence, the SI unit for wave velocity is
 $\Rightarrow m \times {s^{ - 1}} = m{s^{ - 1}} = m/s $
Which is in full called metres per second.