Relationship between velocity, frequency and wavelength of a wave

Important terms used in wave motion

(i) Wavelength (λ)

The distance travelled by a wave during which a particle of the medium completes one vibration is called wavelength. It is also defined as the distance between any two nearest particles on the wave having same phase.

Wavelength may also be defined as the distance between two successive crests or troughs in transverse waves, or the distance between two successive compressions or rarefactions in longitudinal waves.

(ii) Time period (T)

The time period of a wave is the time taken by the wave to travel a distance equal to its wavelength.

(iii) Frequency (n)

This is defined as the number of waves produced in one second. If T represents the time required by a particle to complete one vibration,

then it makes1/T  waves in one second.

Therefore frequency is the reciprocal of the time period (i.e) n = 1/T.

Relationship between velocity, frequency and wavelength of a wave

The distance travelled by a wave in a medium in one second is called the velocity of propagation of the wave in that medium. If v represents the velocity of propagation of the wave, it is given by

_{Velocity = Distance travelled / Time taken}

v = λ/T = n λ

The velocity of a wave (v) is given by the product of the frequency and wavelength.