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Difference between Wavelength and Frequency

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Wavelength is the distance between two wave crests, and it will be the same for troughs and 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). 

In this article, we will learn about, Wavelength Definition, Wavelength Formula, Frequency Definition, Frequency Formula. Difference between Wavelength and Frequency and others in detail.

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).

Wavelength Definition

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 Formula

Wavelength of any wave is given by the formula,

λ = v/f

where,

  • λ is Wavelength of Wave
  • v is Velocity of Wave
  • f is Frequency of Light

What is Frequency (f)?

Number of wave vibrating in a unit second is called the Frequency. It is measured in Hertz(Hz). 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 Definition

Frequency of any wave is the number of oscillation that a wave perform in a second. We can also define the frequency as the number of waves that passes a fixed point in the unit time.

Frequency Formula

Frequency of the wave is calculated using the formula,

f = 1/T

where, T is the Time Period of Wave

Relation Between Frequency, Wavelength, and Speed of Wave

Relation Between Frequency, Wavelength, and Speed of Wave is added below,

Speed = Frequency × Wavelength 

v = f × λ

where, 

  • f is the Frequency of Wave
  • v is the Velocity of Wave
  • T is the Time Period of Wave

Therefore, the above relation is interpreted for frequency as,

f = c/λ

And in terms of wavelength it is represented as,

λ = c/f

Difference between Wavelength and Frequency

Difference between Wavelength and Frequency of the wave are added in the table below,

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. 

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Problems On Wavelength and Frequency Formula

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

Solution:

Given,

  • Speed = 10 m/s
  • Frequency = 5 Hz

Using Formula, 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 Formula, 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 Formula, 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 Formula, 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 Formula, c = λ × f

= 50 × 10

= 500 m/s

Thus the speed is 500 m/s.

FAQs on Wavelength and Frequency

1. What is the Difference between Wavelength and Frequency?

The difference between Wavelength and Frequency is that wavelength is the distance between two points in phase while frequency is the number of oscillations per unit of time

2. What is the Simple Definition of Wavelength?

Wavelength is the distance from one crest to another, or from one trough to another, of a wave.

3. What is Unit to measure the Wavelength of a any Wave?

As, wavelength is the length between two trough and crest of wave so it is measured in unit of length and the wavelength of any wave is generally measured in Angstrom (A).

4. What is Simple Definition of Frequency?

Frequency of any wave is the number of oscillation that the wave completes in one second.

5. What is the Unit to measure the Frequency of any Wave?

Frequency of any wave is measured in sec-1 or hz (hertz).

6. What is the Relationship between Wavelength and Frequency?

Wavelength and Frequency are related as wavelength = wave velocity /Frequency



Last Updated : 04 Feb, 2024
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