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Wavelength

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Wavelength is a fundamental property of a wave. To begin with the wavelength, one has to know about the properties of a wave. The study of waves included in wave mechanics. Basically, wave mechanics is a mathematical treatment of the behavior of small particles and involves the application of a fundamental concept in physics, namely the concept of wave.

Two important principles lay the foundation of wave mechanics, the dual nature of matter and the Heisenberg uncertainty principles. Later, the mathematics of wave mechanics was developed by various workers, the most popular of which, however, is the one initiated by Schrodinger in 1926 and subsequently developed by others.

Wavelength Definition

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Wavelength is the distance between two peaks of the crest or trough of a wave. Wavelength is denoted by $\lambda$ and it is measured in meters. Wavelength is well related to the velocity of light and the frequency of the wave.

Wavelength

The mathematical expression for the wavelength is,
$\lambda$ = $\frac{c}{f}$

where,
$\lambda$ is the wavelength,
c is the velocity of light,
f is the frequency of wave.
Wavelength spectrum is nothing but the spectrum which is arranged according to the wavelength or frequency of waves. The spectrum is illustrated below:

Wavelength Spectrum

The given figure shows the ranges of different spectra. According to the wavelength, the colour is also different. In the case of visible spectrum, the violet colour lies in the wavelength range 380-450nm. The ranges according to the colour of visible spectra is given in the next section.
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Light waves have different wavelength according to their colour. There is a particular range in the case of every colour. The range is, 380-450nm violet; 450-495nm blue; 495-570nm green; 570-590nm yellow; 590-620nm orange; 620-750nm red. A light wave does not need a medium to propagate. This propagation carries energy from one point to another. Infrared light has a longer wavelength and short frequency than visible light. But ultraviolet light has small wavelength and high frequency compared to the visible light.
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Wavelength of Sound

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Basically we are considering the frequency when we are talking about the sound. Wavelength and frequency are inversely proportional to each other. According to the frequency, there are different sounds. The range of sound audible to the human ear is 20Hz to 20kHz. The sound which is above this range is known as ultrasonic sound.

Wavelength to Energy

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From the given equation one can understand the relation between the wavelength and energy. This expression is derived from Einstein's mass energy relation; the equation is given as,

E = $\frac{hc}{\lambda}$
where,
h is the Planck's constant,
c is the light velocity,
$\lambda$ is the wavelength.

So, if we know the wavelength of a wave we can calculate the frequency.

Calculate Wavelength

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Some solved problems are mentioned below which helps to provide more idea about the topic.

Solved Examples

Question 1: Calculate the wavelength of a light wave if the frequency is 1500Hz?

Solution:
 
Given that,
Frequency of a light wave, f = 1500Hz
We know that, velocity of light, c = 3×108m/s

The equation for finding wavelength is,
$\lambda$ = $\frac{c}{f}$
$\lambda$ = $\frac{3 \times 10^8}{1500}$
$\lambda$ =2 $\times $ $10^5$m

 

Question 2: Frequency of a wave is given as 500Hz, determine its wavelength?

Solution:
 
Given that,
Frequency of a light wave, f = 500Hz
We know that, velocity of light, c = 3×108m/s

The equation for finding wavelength is,
$\lambda$ = $\frac{c}{f}$
$\lambda$ = $\frac{3 \times 10^8}{500}$
$\lambda$ = 6 $\times $ $10^5$m