JUMP TO TOPIC

# 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 cycle**. The 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.