Difference Between Wavelength and Frequency

Wavelength vs Frequency
 

Frequency and wavelength are two phenomena encountered in wave mechanics. The frequency of an oscillation describes how “frequent” the event is. The wavelength of a wave describes the length of a unit wave. Both of these concepts are very important in understanding fields such as wave mechanics, modern physics, quantum mechanics and electromagnetic field theory. It is vital to have a clear understanding in these concepts in order to excel in such fields. In this article, we are going to discuss what frequency and wavelength are, their definitions, the similarities of wavelength and frequency and finally the difference between wavelength and frequency.

Frequency

Frequency is a concept discussed in periodic motions of objects. To understand the concept of frequency, a proper understanding of periodic motions is required. A periodic motion can be considered as any motion that repeats itself in a fixed time period. A planet revolving around the sun is a periodic motion. A satellite orbiting around the earth is a periodic motion; even the motion of a balance ball set is a periodic motion. Most of the periodic motions we encounter are circular, linear or semi-circular. A periodic motion has a frequency. The frequency means how “frequent” the event is. For simplicity, we take frequency as the occurrences per second. Periodic motions can be either uniform or non-uniform. A uniform can have a uniform angular velocity. Functions such as amplitude modulation can have double periods. They are periodic functions encapsulated in other periodic functions. The inverse of the frequency of the periodic motion gives the time for a period. Simple harmonic motions and damped harmonic motions are also periodic motions. Thereby the frequency of a periodic motion can also be obtained using the time difference between two similar occurrences. The frequency of a simple pendulum only depends on the length of the pendulum and the gravitational acceleration for small oscillations.

Wavelength

Wavelength is a concept discussed under waves. The wavelength of a wave is the length where the shape of the wave starts to repeat itself. This can be defined using the wave equation. For a time dependent wave equation ψ(x, t), in a given time, if ψ(x, t) is equal for two x values and there are no points between the two points having the same ψ value, the difference of x values are known as the wavelength of the wave. The relationship between the wavelength, frequency and the velocity of the wave is given by v = f λ, where f is the frequency of the wave and λ is the wavelength. For a given wave, since the wave velocity is constant, the wavelength becomes inversely proportional to the frequency.