Free · Acoustic waves calculators 🔊

Two-Wave Frequency Difference & Beats

Find the nonnegative difference frequency between two waves or solve a higher-frequency inverse branch.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Waves at 440 Hz and 443 Hz have a beat frequency of 3 Hz. Equal frequencies give zero beats per second.

Beat frequency = absolute value of (f₂ − f₁)

Worked example

Enter these known values and leave the other values blank.

First wave frequency
440 Hz
Second wave frequency
443 Hz
Difference / beat frequency
3 Hz

Assumptions and limitations

  • Wave and beat frequencies must be nonnegative. Ordinary frequency in hertz counts cycles per second.
  • When one wave frequency and the beat frequency are supplied, the retained inverse returns known frequency plus beat frequency. A lower nonnegative frequency may also satisfy the absolute-difference equation.
  • The number is a frequency difference. Slowly audible beating additionally depends on sufficiently close frequencies, superposition and the listening situation.

Common questions

Can beats alone tell whether a second tone is higher or lower?

No. A 3 Hz difference from 440 Hz can correspond to 437 Hz or 443 Hz. The inverse field returns the higher branch, 443 Hz.

What happens if I swap the two frequencies?

The beat frequency stays the same because the formula takes an absolute difference.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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