 # Wavelength Formula

The distance between consecutive crests of a wave, particularly the points of an electromagnetic wave is known as its wavelength. The wavelength and frequency are closely related. Higher the frequency, shorter is the wavelength. Since all the light waves move through a vacuum with the same speed, the number of wave crests passing by a given point per second depends on the wavelength.

The Wavelength is denoted by λ. The Wavelength Formula of any wave is given by

#### λ = v/f

Where,

V= velocity of the wave

f = frequency

The Wavelength is expressed in m, velocity is expressed in m/s, frequency is expressed in Hz.

Example 1

A harmonic wave is moving along a rope. The source generating the waves completes 50 to and fro motions in 20 s. A trough travels 3m in 4s; determine the wavelength of the wave.

Solution:

Time taken for 50 oscillations = 20 s

Time for 1 oscillation, t = 20/50= 0.4 s

Frequency of 1 oscillation, f = 1/0.4 = 2.5 Hz

The wave travels a distance of 3m in 4s.

The wave speed is calculated by v = 3 / 4

= 0.75 ms-1

The wavelength formula is given by λ = v / f

= 0.75/2.5

λ  = 0.3 m.

Example 2

The frequency of a tuning fork is 200 Hz and sound travels a distance of 20 m while tuning fork executes 30 vibrations. Determine the wavelength of sound.

Solution

Given:

Frequency f = 200 Hz,

Distance d = 20 m,

No of vibrations/ oscillations = 30

Wavelength λ = Distance / No of oscillations

= 20 / 30

λ  = 0.66 ms-1