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(λ): Wavelength is defined as the distance over which the shape of a wave repeats. It is the spatial period of the wave, measured in meters. Essentially, it is the length of one complete cycle of the wave, from one peak to the next.
Frequency(f): Wave frequency refers to the number of complete cycles (compressions and rarefactions) that occur in a unit of time. It is typically measured in Hertz (Hz), where one Hertz is equivalent to one cycle per second. Frequency determines the pitch of a sound; higher frequencies correspond to higher-pitched sounds, while lower frequencies yield lower-pitched sounds.
Wave Velocity(v): Wave velocity is a measure of how fast a sound wave propagates through a given medium. It is usually expressed in meters per second (m/s). The velocity of sound varies depending on the medium through which it travels. In general, sound travels fastest through solids, slower through liquids, and slowest through gases.
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.
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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 Questions
Q1: 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?
Q2: 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?
Q3: 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?
Q4: 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?
FAQs on Wavelength of Sound?
How do you find the speed of sound in air?
The speed of sound in air is approximately 343 meters per second at room temperature (20°C).
What units should be used for the speed of sound and frequency?
The speed of sound should be in meters per second (m/s) and the frequency in hertz (Hz).
How does temperature affect the speed of sound?
The speed of sound increases with temperature; it is approximately
331.3+0.6T m/s, where T is in degrees Celsius.
Does frequency affect the wavelength of sound?
Yes, higher frequency sound waves have shorter wavelengths and lower frequency sound waves have longer wavelengths.