Wavelength and frequency are two important characteristics to explain the nature of a wave. Wavelength is basically the measure of the distance between two successive points referred to as crests or troughs of a wave. It is always measured in the direction of the wave and is represented by the symbol [lambda ]. Since it is a measure of the length of distance, it is expressed a unit of length, i.e., meters. Mathematically, it is the speed of the wave in a medium divided by the frequency of the wave.
Frequency of a wave is the number of occurrences of events per unit time. Mathematically, it is the reciprocal of the time period. Frequency is represented by the symbol ‘f’ and its unit is Hertz (Hz). In the context of waves, it can be defined as the number of waves that can pass a certain fixed point per unit of time.
Relationship Between Wavelength and Frequency
The wavelength of a wave is inversely proportional to its frequency. If v represents the velocity of a wave, its frequency f, and its wavelength[lambda ], then;
[lambda = frac{v}{f}]
This means, as wavelength increases, the frequency will decrease and vice versa.
In the case of light in a vacuum, this formula is given as [lambda ]=cν
Practice Questions:
Example 1: A typical sound wave traveling at 360 m/s has a frequency of 1200 Hz. Find its wavelength.
Solution:
[nu ] = 1200 Hz, v = 360 m/s, [lambda ]=?
[lambda = frac{v}{nu } = frac{{360}}{{1200}} = 0.3,m]
Example 2: All electromagnetic waves travel through a vacuum at the same speed. If a wave of frequency 7.5 GHz has a wavelength of 4 cm, then the frequency of a wave with wavelength 6 km will be (assume both are electromagnetic waves propagating in vacuum):
Options:
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40 kHz
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50 kHz
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5 GHz
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2.5 MHz
Answer: (b)
Conclusion
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