Question

Derive the relation between the velocity of the wave, wavelength, and frequency.

Answer 1

Hint : Waves travel through different waves through different mediums in terms of oscillation of particles or fields. The wavelength of a wave is related to the distance between two peaks of a wave while the frequency of the wave is associated with the number of times a point in the wave oscillates in one second.

Complete step by step answer
We will answer this question by using the definition of different aspects of a wave. In a travelling wave,
The velocity of the wave is the ratio of the distance travelled by the wave to the amount of time the wave takes to travel that distance.
The wavelength of a wave is the distance the wave is covered by the wave in one time period. It can also be thought of as the distance between two peaks or crests of the wave as it traverses that distance in one time period.
The frequency of a wave is the inverse of its time period. It can be thought of as the number of cycles a wave goes through per second. Since the velocity of the wave can also be thought of as the ratio of the wavelength which is the distance travelled by the wave in one cycle to the time period of the wave, we can write
 $\Rightarrow {\text{Velocity = }}\dfrac{{{\text{Wavelength}}}}{{{\text{Time}}\,{\text{period}}}} $
Since the frequency of a wave is the inverse of its time period, we can say
 $\Rightarrow {\text{Velocity = Wavelength}} \times {\text{Frequency}} $
Hence, we have the relation between velocity, wavelength, and frequency of the wave.

Note
Waves can travel in the form of transverse or longitudinal waves. The type of wave decides whether the components of the wave will be displaced in a direction parallel to the direction of propagation or perpendicular to it. Regardless, the relation between the velocity, wavelength, and frequency of a wave remains the same for both kinds of waves.