Wavelength Formula

It is a fundamental concept in physics for understanding wave equations and various laws pertaining to frequency and waves. This article sheds some light on the basics of this formula.
Physics students are introduced to the concept of wavelength in the chapters related to waves. Generally, when we talk of waves in physics, the mathematical picture that comes to our mind are graphs of standard trigonometric functions like sine and cosine waves. The crests and troughs of a wave are used to define wavelength, and hence frequency. It is a useful tool in solving arithmetic problems related to wave functions and in determining the frequency of various waves that are a part of the electromagnetic spectrum.

What is Wavelength?
There are various parameters that govern the characteristics of a wave like speed, amplitude, time period and frequency. Interrelated to these factors are wavelength, a physical quantity that is represented by the Greek letter λ (lambda). Generally, wavelength in physics is defined as the numerical distance between two adjacent crests or troughs. Some waves are periodic, that is there is a uniformity in them and the graph repeats itself at fixed intervals of time. For example, consider the sine function f(x) = sinx, where x= 0, 2π, 3π,...nπ. It is a periodic function with the period 2π. In non-periodic functions, the value of time period is not constant. That means, if you visualize the graph of any non-periodic function, it won't repeat itself at regular intervals of time.

The concept of waves, as we all know, is not new. Ever since Sir Issac Newton used a prism to split sunlight into fundamental colors of rainbow, research and studies on waves have been a part of physics. Physicists such as Sir William Herschel, Johann Ritter, Michael Faraday, James Maxwell, Wilhelm Rontgen and Albert Einstein were other scientists whose pioneering works further made valuable contributions in understanding waves, and hence wavelengths.

So, what is wavelength? Wavelength is defined as the distance occupied by one cycle of wave at any instant. As mentioned earlier, it's the distance occupied between two regular crests or troughs of a wave. Wavelength can be measured in many ranges, from few hundredths of an inch to meters. The wavelength formula, also called wavelength frequency formula, is given below,

λ = c/f where,

Lambda (λ) = wavelength in any unit of length (generally meter)
v = velocity of light = (m/s)
f = frequency in Hz

Here, we need to understand the definition of frequency. Frequency is defined as the number of times a wave passes through a point per second. Frequency is measured in hertz (Hz). The frequency formula is given by,

f = I/T, where,

T = time of wave period in one cycle (in seconds)
f = frequency in Hz

In the field of quantum physics, this formula is interpreted in different terms and is related to Planck's constant and energy of a photon. Planck's constant is a unit that describes smallest measurable unit in relation to a photon. Firstly, let us have a look at the first equation,

E = hc/λ

E = Energy of the wave
h = Planck's constant
c = speed of light
λ = wavelength

The second equation, that is indirectly the same as the first, and can be used by varying this formula, λ = c/f is,

E = hf (substituting, c/λ in E = hc/λ by f, using wavelength formula λ = c/f)

Besides these, there are various formulas for calculating wavelength in higher order wave equations that are just a modification of the basic ones, and are used in higher physics classes. The forumula, in its most basic form, is mentioned in this article and is used in elementary physics in schools and colleges.
Last Updated: September 27, 2011
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