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Difference between Wavelength and Frequency

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  • Last Updated : 26 May, 2022

We know that both electric and magnetic fields travel in waves and that the interruption of these fields is referred to as light. When you toss a stone into a pool, for example, we can see the waves in a circular pattern moving outward from the stone. Every light ripple, like these waves, has a series of high points known as crests where the electric field is strongest, and a series of low places known as troughs where the electric field is weakest. The wavelength is the distance between two wave crests, and it will be the same for troughs. The frequency is the number of vibrations that pass over a given spot in one second, and it is measured in cycles per second (Hz) (Hertz). 

Wavelength-vs-Frequency

The relation between wavelength and frequency is discussed in this article. Waves have a variety of features that can be used to define them. Two such properties are wavelength and frequency. As we’ll see below, the link between wavelength and frequency is that the frequency of a wave multiplied by its wavelength yields the wave’s speed.

What is Wavelength (λ)?

The distance between two close points that are in phase with each other is defined as a wavelength. As a result, a single wavelength separates two consecutive peaks on a wave that would otherwise be a trough. A wave’s wavelength is represented by the symbol lambda (λ). 

The wavelength of a wave is the distance between two crests or troughs. The crest is the highest point on the wave, while the trough is the lowest point. Meters, centimeters, millimeters, nanometers, and other wavelength units are used.

Wavelength is given by the formula:

λ = v/f

where,

  • v is the speed and 
  • f is the frequency of light.

What is Frequency (f)?

The number of wave vibrations for each unit time calculated in Hz is known as frequency. 

Humans can hear frequencies ranging from 20 Hz to 20000 Hz. Ultrasound refers to sound frequencies that are above the range of human hearing. Infrasound is the term for sound frequencies that are below the range of human hearing.

Frequency is given by the formula:

f = 1/T

where,

  • T is the Time period.

Relation Between Frequency, Wavelength, and Speed of Wave

Since the speed of light is defined as:

Speed = Frequency × Wavelength 

or 

c = f × λ

where, 

  • f is the frequency of the wave, 

Therefore, the above relation is interpreted for frequency as:

f = c/λ

And in terms of wavelength is:

λ = c/f

Difference between Wavelength and Frequency 

Frequency 

Wavelength

Frequency is defined as the number of complete wave cycles per second.Wavelength is defined as the total distance covered to complete one wave.
It is a measure to determine Time.It is a measure to find the Distance.
It is denoted by the symbol f. It is denoted by the symbol λ. 
The formula to calculate the frequency is, f = c/λ, where c is the speed of light.The formula to calculate the frequency is, λ = c/f, where c is the speed of light.
The SI unit of f is Hertz (Hz).The SI unit of λ is meter (m).
Frequency is used to measure the recurrence of sound waves.Wavelength is used to measure the length of sound waves.
 Frequency can be determined for both waves and vibrations and for any periodic motion. Wavelength is only limited to a wave. 

Sample Problems

Problem 1: Find the wavelength of a wave traveling at 10 m/s at a frequency of 5 Hz?

Solution:

Given that,

Speed = 10 m/s

Frequency = 5 Hz

Using the formula we have,

λ = c/f

= 10 / 5

= 2 m

Thus, the wavelength is 2 m.

Problem 2: Find the wavelength of a wave traveling at 60 m/s at a frequency of 12 Hz?

Solution:

Using the formula we have,

λ = c/f

= 60 / 12

= 5 m

Problem 3: Find the wavelength of a wave traveling at 100 m/s at a frequency of 11 Hz?

Solution:

Using the formula we have,

λ = c/f

= 100 / 11

= 9.09 m

Problem 4: What is the frequency of light with a speed of 2.998 × 108 ms-1 and a wavelength of 400 nm?

Solution:

Using the formula we have,

f = λ/c

= 2.998 x 108 ms-1 /  400 x 10 -9 m

= 7.50 x 1014 Hz

Problem 5: A wave has a frequency of 50 Hz and a wavelength of 10 m. What is the speed of the wave?

Solution:

Using the formula we have,

c = λ × f

= 50 × 10

= 500 m/s

Thus the speed is 500 m/s.

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