How to Calculate the Wavelength of Sound?

The wavelength of sound refers to the distance between two points in a sound wave that are in sync. To find the wavelength, you can use this formula: Sound Wavelength (λ) = Speed of Sound (v) ÷ Frequency of Sound (f). In this formula, wavelength is measured in meters (m), speed of sound is in meters per second (m/s), and frequency is in hertz (Hz).

Sound waves are a type of wave that travels through materials like air, water, or solids. They move quickly through solids, slower through liquids, and even slower through gases. For example, sound travels at 343 m/s in air, 1403 m/s in water, and 1007 m/s in helium.

How do you Calculate the Wavelength of Sound?

To calculate the wavelength of sound, you can use the formula:

λ = v/f

Where:

• λ = Wavelength of sound (in meters)
• v = Speed of sound (in meters per second)
• f = Frequency of the sound wave (in Hertz)

Sound has three main characteristics:

Wavelength: The distance over which a sound wave pattern repeats itself, measured in meters.

Frequency: The number of wave cycles per second, measured in Hertz.

Velocity: How fast the sound wave travels through a medium, measured in meters per second.

To calculate the wavelength, remember that it’s the distance between two identical points on the wave. You can use the formula mentioned earlier to find it. The symbol for wavelength is λ, and it’s measured in meters (m).

Sound Wavelength Formula

The formula of calculate 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.

Sample Problems

Problem 1: How long is the wavelength of a sound wave traveling through the air if it has a frequency of 20 Hz?

Solution:

Given:

Speed of sound in air (v) = 343 m/s (you can think of this as how fast sound travels in air)

Frequency of sound wave (f) = 20 Hz (this tells us how many wave cycles occur in one second)

Using the formula for wavelength (λ = v / f), we substitute the given values:

Wavelength (λ) = Speed of sound (v) / Frequency (f)

Wavelength (λ) = 343 m/s / 20 Hz

Wavelength (λ) ≈ 17.15 meters

Therefore, the wavelength of the sound wave in air is approximately 17.15 meters.

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?