# Sound Wavelength Calculator

Created by Luis Hoyos
Reviewed by Hanna Pamuła, PhD candidate and Steven Wooding
Last updated: Apr 20, 2022

Waves are everywhere, and as sound is a mechanical wave present in many essential aspects of our lives, we created the sound wavelength calculator.

Our sound wave calculator lets you know the wavelength of a sound wave if you know its frequency and speed (or the medium in which it's propagating). You can also use it to calculate the frequency of a wave if you know its wavelength and sound speed.

Keep reading if you want to learn more exciting aspects about sound waves, how to find the wavelength of sound, and how to calculate the speed of sound with frequency and wavelength.

## The nature of sound waves

Waves are everywhere and manifest in different ways. Waves occur when there's a disturbance in a system, and the disturbance travels from one place to another.

There are two main kinds of waves: mechanical waves and electromagnetic waves. The main difference is that mechanical waves need a medium to travel (a material), whereas electromagnetic waves can travel through a vacuum space.

Sound is an example of a mechanical wave, and other examples include ripples on the water's surface, seismic shear waves, and water waves. Examples of electromagnetic waves are light, microwaves, and radio waves.

Mechanical waves are classified within three groups, depending on the direction of the periodic motion relative to the movement of the wave:

• Longitudinal waves: Each particle moves back and forth in the same direction as the wave.
• Transverse waves: The particles move back and forth transversely (at right-angles) to the wave motion.
• Combined waves: These are a combination of longitudinal and transversal waves. The most common example of this type is sea waves.

Longitudinal waves are the most relevant in our daily lives as, when a fluid acts as the propagation medium, sound waves are longitudinal. Also, sound waves can behave as longitudinal and transversal when the medium is a solid material.

As you may imagine, the study of sound waves is mainly concerned with how it propagates through that strange fluid called air, as that's how we usually receive sound.

Do check out our modulation calculator for info on how waves carry information.

## Wavelength, frequency, and speed: the main components of the sound wave calculator

Pressure disturbance is the cause of sound waves, and we can represent them as sine waves, characterized by three terms:

• Speed of sound: Indicates the speed at which the sound wave propagates. It varies depending on the propagation medium.
• Wavelength: This is the distance between one point to the corresponding point on the following repetition of the wave shape, and it's what we're mainly concerned about in our sound wavelength calculator.
• Frequency: Number of times the wave repeats per unit time, usually measured in Hz. For example, if a wave repeats ten times in a second, it has a frequency of 10 cycles per second or 10 Hz.

Read the following section to know how these variables relate to each other through the sound wavelength formula.

## Sound wavelength formula: sound frequency and wavelength relationship

The wavelength formula of sound is the same used for other waves:

$\quad\ \ λ=\frac{v}{f}$

where $λ$ is the wavelength of the sound wave, $v$ its speed (in this case, speed of sound), and $𝑓$ its frequency.

There are other ways to express this relationship of wavelength and sound frequency. For example, if we wanted to calculate the frequency of a wave, we would rearrange the equation to obtain the frequency of sound formula:

$\quad\ \ f=\frac{v}{λ}$

Finally, if you want to know how to calculate the speed of sound with frequency and wavelength, this is the formula:

$\quad\ \ v=λf$

🔎 Are you further interested in sound speed? Look at our speed of sound calculator. With this tool, you can calculate the speed of sound for air and water, not with frequency and wavelength, but in terms of temperature.

Now that you know the equation of frequency of sound waves and speed of sound, let's look at some exciting aspects about frequency, typical values of the speed of sound, and how to find a sound frequency and wavelength using the calculator.

## Exciting aspects about the frequency and wavelength of sound waves

The frequency of a sound determines how we perceive it. High-pitch sounds are indicative of high frequency, while a low-pitch implies low frequency.

On the other hand, the wavelength is not a dependent quantity, as it depends on the speed of sound (inherent to the environment) and frequency (inherent to the source of the disturbance).

However, we can relate wavelength to the size of the musical instruments. Small size instruments, such as flutes, have a high pitch, and therefore, high frequency and short wavelength. Whereas large instruments, such as trombones, produce long-wavelength sound.

💡 We can say the pitch of a sound (such as the sound produced by musical instruments) is directly related to its frequency. On the other hand, the size of an instrument is related directly to its audio wavelength.

### Frequency ranges of infrasound, acoustic, and ultrasound waves

Frequency doesn't only determine how we feel or perceive a sound but also determines if we can sense it. The human ear cannot perceive all sound waves, and we can only perceive sounds with frequencies from 20 Hz to 20,000 Hz. This spectrum of frequencies is known as the human hearing range.

Nevertheless, frequencies outside the human range are present in our daily lives, both in nature and technology.

### The infrasound range

Although we believe we can hear all the sounds emitted by elephants, most of the sounds produced by these animals are low-frequency noises below 20 Hz, known as infrasound. They use these signals to communicate over distances up to 10 km.

Some natural phenomena also emit infrasound, such as volcanic eruption (below 20 Hz) and earthquakes (below 10 Hz). Curiously, some animals can perceive this range of sound waves, which is why elephants flee in fear when earthquakes events are about to occur.

### The ultrasound range

Have you heard the term "ultrasound imaging" and don't know why it's called that way? Ultrasound imaging uses ultrasound waves to obtain images of the body's internal organs, which can be used, for example, to calculate the volume of your bladder. When a sound wave strikes the targeted object, it bounces back, and with these echoes, physicians construct images of the organs. Ultrasound waves also have applications in therapeutic procedures, and cancer therapy is one of the more promising areas. These applications range mainly from 1 to 3 MHz, but we can even find frequencies up to 7.5 MHz.

The property that describes how much is reflected and the resistance that the ultrasound wave finds through different body tissues is known as acoustic impedance (Z).

In science and technology, we can also use ultrasound for imaging processes in the field of non-destructive testing procedures, such as acoustic microscopy.

Most of the animals are only sensitive to frequencies above the human range. For example, the audible range of dogs 🐶 goes from 67 Hz to 45 kHz, while for cats, from 48 Hz to 85 kHz 🙀

💡 Did you know? Human hearing is sensitive to very low-frequency sound waves compared to most of the frequency emitted by animals. This sensitivity was crucial to the survival of our ancestors, as it allowed us to hear night predators we couldn't see.

## Typical speeds of sound

The speed of sound in a fluid depends on a measure of resistance to compression called bulk modulus ($B$) and its density ($ρ$):

$\quad\ \ v=\sqrt{\frac{B}{ρ}}$

In solids, the speed of sound relationship is similar and depends on a measure of tensile or compressive stiffness called Young's modulus ($E$) and its density:

$\quad\ \ v=\sqrt{\frac{E}{ρ}}$

In both cases, the more resistant the material is, the greater the speed of sound, and the denser the material is, the lower the speed. Temperature is another crucial factor in the speed of sound in fluids, as it affects bulk modulus and density.

Anyway, you don't have to bother with calculating the speed of sound on your own. Our sound wavelength calculator provides you in advance with the speed of sound in different materials, for example:

• Air (20 °C/68 °F): 343 m/s
• Water (20 °C/68 °F): 1481 m/s
• Aluminium: 6420 m/s

## How to find the wavelength of sound using the sound wavelength calculator

Let's suppose you want to calculate the wavelength of a woman's voice in the air. If we know the average frequency of the women voice is 210 Hz, these would be the steps:

1. Establish the medium in which your sound wave propagates. In this case, the medium could be air at 20 °C.
2. Input 210 Hz in the frequency box.
3. Now you're done with your sound wave calculation! The result should be 1.6333 m.

You can also select the air as your medium, lock it, and convert our sound wavelength calculator into a sound wavelength in air calculator 😜

This calculator also works the other way, so if you don't know how to find the sound frequency, you only have to follow the same previous steps but input the audio wavelength instead of the frequency in the calculator.

Luis Hoyos
Medium
Air (20 °C/68 °F)
Speed of sound (v)
m/s
Frequency (𝑓)
Hz
Wavelength (λ)
m
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