Derive the Equation of the speed of sound

The distance by which a point on the wave, such as compression or rarefaction, travels in unit time is called the speed of the sound wave.

Consider the definitions of time period (T) and wavelength λ. We can write the following:

Let the distance traveled by a wave in T seconds = λ meters
The distance traveled by a wave in 1 second = T/λ meters.

Thus by definition, the speed of sound wave v = λ/T ……………………. (1)

We know that frequency υ =1/T …………………………. (2)

From equation (1) & (2) we get v = υ λ ………………. (3)
=> Speed of a sound wave = frequency x wavelength [derivation done]

Note:

The speed of a sound wave depends on the properties such as the temperature and nature of the medium in which it is traveling. However, the speed of sound remains almost the same for all frequencies in a given medium under the same physical conditions.