Wavelength Formula
What is Wavelength?
In physics, wavelength is a basic property of wave propagation, be it a sound wave, light wave, or any other wave whatsoever. In plain words, the wavelength means the distance between successive points in phase on adjacent oscillations, such as peaks or troughs, of a wave.
The Wavelength Formula
The wavelength formula is given as,
where:
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λ (lambda) is the wavelength, measured in meters (m) or other length units.
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v is the wave velocity, measured in meters per second (m/s).
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f is the wave frequency, measured in Hertz (Hz).
Solved Problems
Problem 1: A harmonic wave is moving along a rope. The source generating the waves completes 50 to and fro motions in 20 seconds . A trough travels 3m in 4s; calculate the wavelength of the wave.
Solution:
Time taken for 50 oscillations = 20 seconds
Time for 1 oscillation, t = 20/50= 0.4 seconds
Frequency of 1 oscillation, f = 1/0.4 = 2.5Hz
The wave travels a distance of 3m in 4s.
The wave speed is calculated by v = 3 / 4
= 0.75 ms-1
By using wavelength formula ,we get
λ = v / f
= 0.75/2.5
λ = 0.3 m.
Problem 2: The frequency of a tuning fork is 200 Hz and sound travels a distance of 20m while the 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
Conclusions
The formula for wavelength is a strong tool in the understanding of wave behavior, the way it interacts with the different environments that come into contact with such waves. Being in control of this formula and the different components of it can, in turn, give insight into many physical phenomena and applications in science and technology.
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