Open In App

How to Calculate the Wavelength of Sound?

Improve
Improve
Like Article
Like
Save
Share
Report

Wavelength of Sound is the distance between two successive locations in a sound wave in phase. To calculate the wavelength of sound use the formula Sound Wavelength(λ) = Velocity of Sound(v)/Frequency of Sound(f), where the wavelength of sound is in meters (m), speed of sound in the medium is in meters per second (m/s), and the frequency of the sound wave is in hertz (Hz). In this article, we are going to discuss what sound waves are, sound wavelength, and some sample problems based on this concept.

What is Sound waves?

Sound waves are defined as longitudinal waves that form a pattern of disruptions created by the flow of energy across materials such as air, liquid, or solid. To put it another way, they can be defined as a vibration that travels through the medium as mechanical waves. They travel quickly in solids, slowly in liquids, and very slowly in gaseous media.

The speed of sound waves varies drastically from medium to medium. For example, the speed of sound is 343 m/s in air, 1403 m/s in water, and 1007 m/s in helium.

Characteristics of Sound

The sound can travel fast in solids, slower in liquids, and relatively slowly in gaseous mediums. The three most important characteristics of sound waves are:

  • Wavelength: It is defined as the distance in which the shape of the wave repeats. It is measured in terms of meters
  • Frequency: It is defined as the number of refractions and compressions which occur per unit time. The frequency is measured in terms of Hertz
  • Velocity: It is the measure, which is used to calculate how fast the sound wave propagates in the given medium. The unit of wave velocity is a meter per second.

How to Calculate Sound Wavelength

The wavelength is defined as the distance between the two nearest points in phase with each other. It is defined as the distance over which the shape of a sound wave repeats.

It is represented by the symbol λ (lambda). SI unit is given by meters (m) and its dimensional formula is given by [M0L1T0].

Wavelength of sound can be calculated using the formula discussed below:

Sound Wavelength Formula

The formula of sound wavelength is given below:

λ = v/f

Where,

  • v is the velocity of sound wave,
  • f is the frequency of sound wave.

Derivation of Sound Wavelength

We know that wavelength is the distance travelled by the sound wave at a constant velocity in time t.

λ = vt . . .(1)

Also, it is known that the frequency of a wave is defined as the reciprocal of time.

f = 1/t     

⇒ t = 1/f . . .(2)

Using (2) we get,

λ = v (1/f)

⇒ λ = v/f

This derives the formula for sound wavelength.

Similar Reads

Sample Problems

Problem 1. Calculate the wavelength of a sound wave travelling in air at a frequency of 20 Hz.

Solution:

We have,

v = 343

f = 20

Using the formula we have,

λ = v/f

⇒ λ = 343/20

⇒ λ = 17.15 m

Problem 2. Calculate the wavelength of a sound wave travelling in air at a frequency of 65 Hz.

Solution:

We have,

v = 343

f = 65

Using the formula we have,

λ = v/f

⇒ λ = 343/65

⇒ λ = 5.27 m

Problem 3. Calculate the wavelength of a sound wave travelling in water at a frequency of 5 Hz.

Solution:

We have,

v = 1403

f = 20

Using the formula we have,

λ = v/f

⇒ λ = 1403/5

⇒ λ = 280.6 m

Problem 4. Calculate the wavelength of a sound wave travelling in helium at a frequency of 35 Hz.

Solution:

We have,

v = 1007

f = 35

Using the formula we have,

λ = v/f

⇒ λ = 1007/35

⇒ λ = 28.77 m

Practice Problems

Problem 1: What is the wavelength of a sound wave if the sound travels at a speed of around 343 meters per second through air and has a frequency of 440 Hz?

Problem 2: The frequency of the sound wave produced by a tuning fork is 256 Hz. What is the speed of sound in air if this sound wave has a wavelength of 1.35 meters?

Problem 3: A sound wave’s wavelength in water is measured to be 0.02 meters. What is the frequency of the sound wave if the sound speed in water is around 1482 meters per second?

Problem 4: The fundamental frequency, or first harmonic, of a closed pipe is 440 Hz. What is the length of the pipe if the sound speed within it is 340 m/s?

Problem 5: The speed of sound through water is around 1482 meters per second. How long is the wavelength of a sound wave in water if its frequency is 2000 Hz?


Last Updated : 15 Mar, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads