Question

What is the formula for calculating wave velocity?

Answer 1

Hint: Wave velocity is the velocity with which the wave propagates. It is expressed as a product of wavelength of the wave and frequency of the wave in a medium. In vacuum the velocity of all the electromagnetic waves is the speed of light (c).

Complete step by step answer:
Wave is created usually when particles of a medium oscillate about their mean position either along the wave direction or perpendicular to it. Wave are of two types: 1. Longitudinal waves, in which the direction of propagation of the wave is the same as the particle motion. 2. Transverse waves, where the motion of particles is perpendicular to the propagation of the wave. Now, waves travel with some velocity in a medium. When a particle of that medium completes one full oscillation, it does so in time period T. Therefore, the wave velocity is the distance that the particle of the medium covers in this time. $\text{wave velocity = }{\displaystyle \frac{\lambda }{T}}=\nu \lambda$ Consider the wave motion in a transverse wave. This wave consists of different particles that are performing simple harmonic motion about some mean position. Consider a particle in this wave (see figure). Consider that this particle is represented by Red Dot in the diagram. When the particle starts from this position and as the wave propagates through this point, it comes back to the same position. That helps in defining the velocity of wave propagation.

Note: Wave velocity is also called phase velocity. This means that we are considering how much time, a particle in a wave is able to come back to the same phase where it started. Phase is the respective angular position that a particle of the wave possesses in terms of mean/extreme position.