# Beat Frequency Calculator

Created by Komal Rafay
Reviewed by Dominik Czernia, PhD candidate and Jack Bowater
Last updated: Feb 02, 2022

This beat frequency calculator is a tool that finds the beat frequency of two waves. If you are a music lover, you probably know all about beats, but have you ever wondered what the frequency of the beat you are listening to is? Knowing how to calculate beat frequency helps to understand, e.g., the logic behind the famous binaural beats and their frequencies.

In the article below, you will learn how to use the beat frequency equation and a few significant applications of the beat frequency.

## Beat frequency calculator

The beat frequency calculator is a practical and efficient tool that lets you calculate the beat frequency of two sound waves.

Frequency refers to the occurrence of an event per unit time. Beats are the interference pattern between two waves that differ in frequencies. Thus, the beat frequency is:

The absolute difference between the frequencies of two waves.

The beat frequency calculator takes the frequencies of two sound waves as its input and calculates their beat frequency. For example, the beat frequency of two waves having frequencies 235 Hz and 335 Hz would be 100 Hz.

## What is the beat frequency?

When two waves with similar frequencies travel and coincide in the same medium, they produce beats. The beat frequency, which is the absolute difference between the two waves making the beats, is the rate at which you hear the oscillating volume.

If the two waves differ in their wavelength, then the resulting sound will be irregular and non-repeating, which means it will be unpleasant to listen. Pure beats form if the interfering waves' amplitude are identical; if amplitudes differ, you may not detect beats that easily.

Binaural beats are an exciting kind of beat also known as auditory illusions, and play a role in helping get you to sleep.
They are perceived this way because the tone we hear is a perception of sound made exclusively by our brain. When we hear two waves of different frequencies through each ear, our brain materializes a third sound wave, the one we hear, which is called binaural beat frequency.

Not all beats can be categorized as a binaural beat because there are certain conditions that the waves need to fulfill to produce binaural beats:

• The two waves must have frequencies less than 1000 Hz;
• The beat frequency of the two waves must be less than 30 Hz; and
• Each of the two waves must be heard through the respective ear.

## Beat frequency formula

The main part of the beat frequency equation is the time period of two different waves. The time period of an object is inversely proportional to its frequency, and hence you can deduct one from the other.

Since we understand that the beat frequency is the absolute difference between the frequencies of two waves, we can summarize the beat frequency formula as:

$f_b= |f_2 - f_1|$

where:

• $f_b$ - Beat frequency;

• $f_1$ - Frequency of 1st wave; and

• $f_2$ - Frequency of 2nd wave.

## How to find beat frequency?

To calculate the beat frequency using our calculator, use the following steps:

1. Input the frequency of the first wave.
2. Input the frequency of the second wave.
3. And that's all you have to do! The rest of it is up to the beat frequency calculator. It will find the beat frequency in your selected unit based on the above beat frequency formula.
4. The default unit for frequency is Hertz (Hz).

If you find yourself in a situation where you cannot use the calculator, simply subtract the frequency of the first wave from the frequency of the second wave. The frequencies of either wave can be greater than the other, so to avoid having negative values for every beat frequency, we take the absolute value of the difference of the two waves. This is how to calculate beat frequency in your head.

For example, the frequency of the first wave is 1400Hz and the second frequency is 1560 Hz, the beat frequency will be 160 Hz. Even if the frequency values were reversed, the result would be the same because of the absolute function: the absolute value of -160 is 160.

## Applications of beat frequency

Musicians use the concept of interference beats in tuning their instruments, and the frequency of waves helps with the music scale. Below are some other critical applications:

• Subjective tones
If the beat frequency of two waves or tones is in the mid-frequency range (500 - 2000 Hz), then our ear perceives it as a third wave/tone. This third tone is called the subjective tone.

Radar detectors emit microwave radiations on vehicles and detect the reflected waves. These waves experience doppler effect/shift (they change in frequency in relation to an observer), and the beat frequency of the emitted and reflected waves give the measure of the speed of the vehicle in motion.

• Missing fundamental effect
In music, the fundamental frequency refers to the the lowest frequency that any instrument can produce.
The missing fundamental effect applies to the human capacity to hear the sound of many tones in a situation where the fundamental pitch is either missing or diminished.

• Multiphonics
Have you ever heard a brass instrument played? A single instrument produces three tones, and that is because the musician plays a regular note and a hummed note. The beat frequency of these two notes gives rise to a third tone, which we refer to as multiphonics.

🔊 You might want to check out some more sound and waves calculators:

## FAQ

### How are beats formed?

Beats are formed when two sound waves traveling in the same medium interfere with each other. It causes the sound to alternate between soft and loud tones.

Beats form under the following conditions:

1. The amplitude of the two waves should be identical.
2. The frequency difference must be small.
3. Usually, the difference between frequencies should be less than 10 Hz to hear beats.

### What is the beat frequency of two waves with frequencies 12 Hz and 10 Hz?

The beat frequency of the two waves with frequencies 12 and 10 Hz is 2 Hz. The formula of beat frequency is:

fb = |f2 - f1|

where:

• fb - Beat frequency;
• f1 - Frequency of 1st wave; and
• f2 - Frequency of 2nd wave.

The absolute function in the formula makes the difference always result in a positive value.

### How can I calculate beat frequency?

The beat frequency is the rate of oscillating volume heard. You can calculate it as the absolute difference between two waves. So, if you want to know how to find the beat frequency of two waves:

1. Subtract the first wave's frequency from the second wave's frequency,
2. Take the absolute value.
3. The beat frequency is always a positive value.

### Can sound waves cancel out each other?

Yes, sound waves can cancel each other. The interaction between waves can be constructive and destructive depending on what their wavelengths, frequencies, and relative phases are.

If the peaks line up with troughs, they form destructive waves and cancel out each other. Noise-canceling headphones are based on the destructive waves phenomenon.

Komal Rafay
First wave frequency
Hz
Second wave frequency
Hz
Beat frequency 〰️
Hz
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