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