How is a "beat" created?

When two waves propagate in the same medium and interfere with each other, a "beat" is produced. The loudness varies as sound becomes louder where crests meet, and softer where crest meets trough. The closer the two frequencies are to one another, the slower the variation.

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

The beat frequency is 2 Hz. The beat frequency is the absolute value of the difference between two frequencies, and the absolute value of 12 minus 10 is 2, which means that you would hear a beat twice per second.

How to calculate beat frequency manually?

One frequency is subtracted from the other and the absolute value is taken. Since the absolute value always results in a positive value, order does not matter. Whether one calculates 1560 Hz minus 1400 Hz or 1400 Hz minus 1560 Hz, the beat frequency will be 160 Hz.

Why do you not hear a beat when the frequency difference is large?

Beats are only audible if the difference between the two frequencies is a few hertz. If the frequency difference exceeds about 20 Hz, the variation is too fast to follow and the ear begins to distinguish two separate pitches instead of a throbbing sound.

What is the period of oscillation?

The period is the time between one peak of a sound and the next, and it is the inverse of the frequency. A frequency of 2 Hz repeats every half second. When both frequencies are equal, the frequency becomes zero, and the period is infinite. This means that there is no period.

Beat Frequency Calculator

Your two waves

What do you want to work out?

Two wave frequencies

From wavelengths

Tuning: find an unknown frequency

First wave frequency

Second wave frequency

Beat frequency

Average (carrier) frequency: Hz
Beat period: sec
Envelope frequency: Hz

You would hear the volume throb about

4 Hz, once for every beat.

Beat waveform

The beat frequency calculator computes the slow, wavering sound that results when two waves of nearly identical pitch are superimposed. Given two frequencies it will give you the beat frequency, the beat period and the actual audible average pitch.

It can also be used to calculate based on wavelength or vice versa, for tuning an instrument by a reference pitch.

What is the interference frequency?

When two waves travel through the same medium at the same time they can interfere with each other. When their frequencies are similar, this causes the amplitude of the resulting wave to change regularly.

This change in volume is interference, the number of peaks per second is the frequency of the interference and it equals the difference between the two frequencies.

Formula for interference frequency:

The beat frequency is the absolute value of the difference between two frequencies.

f_{\text{beat}} = \lvert f_1 - f_2 \rvert

Because the result is always a positive number due to the absolute value, it does not matter which wave is referred to as the first one. The beat frequency of two waves with frequencies of 235 Hz and 335 Hz is 100 Hz. The same holds true for 335 Hz and 235 Hz.

There is a deeper reason why the beat frequency matches the result of simple subtraction. When two sine waves are added together they create a single tone with the average frequency and a slowly varying envelope around it.

y = \underbrace{2\cos\!\left(2\pi\,\tfrac{f_1-f_2}{2}\,t\right)}_{\text{envelope}}\;\cos\!\left(2\pi\,\tfrac{f_1+f_2}{2}\,t\right)

The envelope curve oscillates with half the difference frequency but passes through zero twice in a period so that the frequency of the loudness peaks is equal to the full difference. This explains why the beat frequency is equal to the full difference and not just half of it.

In calculating from wavelength, one first converts each wavelength to a frequency using the wave speed and then calculates the difference.

f = \frac{v}{\lambda} \qquad f_{\text{beat}} = \left\lvert \frac{v}{\lambda_1} - \frac{v}{\lambda_2} \right\rvert

Here's how to use this calculator.

Select one of three modes and enter corresponding values in the fields provided.

The direct calculation method uses the frequencies of two waves. Enter in two frequencies to find the beat frequency. The "Calculate from wavelength" option is used when the speed of the wave and the wavelengths of two waves are known.

In the fine tuning mode, the problem is treated in reverse. Enter a known reference frequency and the perceived beat frequency, then select whether the unknown frequency is higher or lower than the reference frequency, and the calculator will return the unknown frequency.

Examples of calculations:

The table shows some waves and their respective oscillation frequencies.

First wave	Second wave	Beat frequency
10 Hz	12 Hz	2 Hz
235 Hz	335 Hz	100 Hz
1400 Hz	1560 Hz	160 Hz
440 Hz	442 Hz	2 Hz

The last line is a typical example of fine tuning. When a stringed instrument with a frequency of 442 Hz plays simultaneously with a reference tone with a frequency of 440 Hz, a vibration occurs twice per second, which leads to an audible impulse of loudness every half-second. By tightening or loosening the string, the beat frequency is reduced to zero.

Applications of the oscillation frequency:

Musicians use the beat frequency to tune instruments. They play a note along with a reference tone and adjust until the phenomenon of "beating" disappears, indicating that both pitches are in tune.

Binaural beats are created by sending slightly different frequencies to the left and right ears, which causes a third lower frequency beat to be produced in the brain. Some people use this for relaxation or concentration purposes. To achieve this effect, both frequencies must be below about 1000 Hz and the resulting beat frequency must be below 30 Hz.

Police radar guns use the beat frequency to determine speed. A radar gun compares the transmitted frequency with the Doppler shifted echo reflected from a moving vehicle. The resulting beat frequency is proportional to the speed of the vehicle.

The beat frequency can also be used to explain combination tones in music, the harshness of dissonances and how noise cancelling headphones cancel one sound wave with another.

Tips for optimal results:

Before comparing two waves make sure you are using the same units. This calculator will convert so you can mix hertz and kilohertz to get accurate results.

A "beat" is most noticeable when the difference between two frequencies is a few hertz and the volume is roughly equal. When the frequency difference exceeds about 20 Hz, the beat becomes a rough rumbling mixture that then separates into two distinct tones.

This tool is for learning and quick estimates. Real rooms have echoes and overtones that cannot be captured with simple sine waves.

Frequently asked questions

How is a "beat" created?: When two waves propagate in the same medium and interfere with each other, a "beat" is produced. The loudness varies as sound becomes louder where crests meet, and softer where crest meets trough. The closer the two frequencies are to one another, the slower the variation.
What is the beat frequency of two waves with frequencies of 12Hz and 10Hz?: The beat frequency is 2 Hz. The beat frequency is the absolute value of the difference between two frequencies, and the absolute value of 12 minus 10 is 2, which means that you would hear a beat twice per second.
How to calculate beat frequency manually?: One frequency is subtracted from the other and the absolute value is taken. Since the absolute value always results in a positive value, order does not matter. Whether one calculates 1560 Hz minus 1400 Hz or 1400 Hz minus 1560 Hz, the beat frequency will be 160 Hz.
Why do you not hear a beat when the frequency difference is large?: Beats are only audible if the difference between the two frequencies is a few hertz. If the frequency difference exceeds about 20 Hz, the variation is too fast to follow and the ear begins to distinguish two separate pitches instead of a throbbing sound.
What is the period of oscillation?: The period is the time between one peak of a sound and the next, and it is the inverse of the frequency. A frequency of 2 Hz repeats every half second. When both frequencies are equal, the frequency becomes zero, and the period is infinite. This means that there is no period.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.