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Frequency to Wavelength Calculator + Online Solver With Free Steps

The Frequency to Wavelength Calculator is used to calculate the wavelength of a sound wave of a particular frequency. To understand the working of this calculator, the user must know what is frequency and wavelength, how are they measured and what is their relationship between them and the speed of light.

The frequency of a sound wave is defined as how many waves pass through a point in one second. A wave cycle is a cycle from crest to crest or trough to trough of a wave. The frequency defines how many wave cycles pass a given point per second. It is denoted by the letter nu “ν”.

The frequency is measured in cycles per second or Hertz “Hz”. Mathematically, the unit of frequency is written as per seconds or s$^{-1}$. The wavelength of a sound wave is the distance measured from crest to crest or trough to trough. It is the distance covered by one wave cycleThe wavelength is measured in meters “m” and is denoted by the Greek letter lambda λ.

The frequency and wavelength have an inverse relationship. The longer the wavelength, the smaller will be the frequency, and the shorter the wavelength the larger frequency.

The speed of light plays an essential role in the relationship between frequency and wavelength. Speed is simply defined as how much time it takes to move from one position to another.

The speed of light is 300 million meters per second. It is denoted by the letter “c” and expressed in scientific notation as 3 × 10$^{8} $ m/s. It is a constant value.

What Is a Frequency to Wavelength Calculator?

The Frequency to Wavelength Calculator is an online tool that is used to compute the wavelength, sound speed, and human hearing threshold by entering the frequency of sound in the air.

The relationship between frequency, wavelength, and speed of light is defined as:

Wavelength × Frequency = Speed of Light

In symbols, it can be written as:

λν = c

For wavelength λ, the equation becomes:

λ = c/ν

The calculator uses this mathematical equation to compute the wavelength λ of a sound wave knowing the frequency ν and speed of light c in air.

How To Use the Frequency to Wavelength Calculator

The user can use the Frequency to Wavelength Calculator by following the steps given below.

Step 1

The user must first enter the frequency of sound in the calculator’s input window. It should be entered in the block labeled Frequency.

The frequency should be in units of cycles per second (/s) or Hertz (Hz) for accurate results. For the default example, the frequency used is 440 Hz.

Step 2

The user must now press the “Submit” button for the calculator to process the value of frequency and compute the output.

Output

The output displayed by the Frequency to Wavelength Calculator is in four headings as given below.

Sound Speed

The Calculator computes the speed of sound at 20°C temperature and 1 atm pressure in dry air. The units used by the calculator are feet per second (ft/s) for sound speed.

For the default example, the sound speed given by the calculator is 1126.5 ft/s.

Wavelength

The calculator uses the mathematical formula for wavelength and frequency and computes the wavelength of sound in air. The wavelength calculated is in meters (m).

The equation is given by:

λ = c/ν

For the frequency ν at 440 Hz, putting the values of c and ν in the above formula gives:

\[ λ = \frac{ 3 × 10^{8} }{ 440 } \]

Simplifying gives:

\[ λ = 6.818 × 10^5 \ \text{meters} \]

So, the wavelength computed by the calculator is 6.818 × 10$^5 $ meters.

Human Hearing Threshold

The Calculator also displays the human hearing threshold for a particular frequency of sound. It is measured in decibels of Sound Pressure Level (dB SPL).

At 440 Hz frequency, the Human Hearing Threshold given by the calculator is 6.8 dB SPL.

Attenuation

The attenuation of sound is defined as the decrease in the strength of the sound wave due to environmental factors such as absorption and scattering.

Attenuation depends upon the medium through which the sound wave passes. It is the decrease in the amplitude and intensity of the wave.

The Calculator also provides the attenuation for higher frequency sound waves. It is measured in decibels of Sound Pressure Level per mile (dB SPL/mile).

Solved Examples

The following examples are solved through the Frequency to Wavelength Calculator.

Example 1

Calculate the wavelength, speed of sound, and the human hearing threshold for the frequency of sound at 670 Hertz.

Solution

The user must enter the frequency of sound in the input tab of the calculator. The frequency given in the example is 670 Hz. After submitting the input frequency, the calculator computes the output as given below.

The speed of sound given by the calculator is 1126.5 feet/second. The wavelength of the sound wave at the particular frequency given by the calculator is 4.477 × 10$^5 $ meters.

The Human Hearing Threshold at the loudness threshold pressure of 20 μPa computed by the calculator is 5.27 dB SPL.

Example 2

The frequency of sound in air is given as 10 kilo-Hz. Compute the sound speed, wavelength, human hearing threshold, and attenuation of the sound wave at this frequency.

Solution

The frequency is given as 10,000 Hz. The user must enter this frequency in the calculator’s input window.

After entering the input sound frequency, the user must press “Submit” for the calculator to calculate the output.

The speed of sound computed by the calculator is 1126.5 ft/s.

The Human Hearing Threshold is given as 16.8 dB SPL at a 20 μPa loudness threshold reference.

The wavelength at the input frequency displayed by the calculator is 3 × 10$^4 $ meters.

The attenuation of the sound wave in the dry air medium is given as 28 dB SPL/mile.

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