Beat Frequency Calculator Formula

Understand the math behind the beat frequency calculator. Each variable explained with a worked example.

Formulas Used

Beat Frequency

beat_freq = abs(f1 - f2)

Beat Period

beat_period = 1 / abs(f1 - f2)

Variables

VariableDescriptionDefault
f1Frequency 1(Hz)440
f2Frequency 2(Hz)443

How It Works

Beat Frequency

When two waves of slightly different frequencies overlap, they produce a pulsating amplitude variation called beats.

Formula

f_beat = f1 - f2

The beat period is T_beat = 1 / f_beat. Beats are commonly used by musicians to tune instruments.

Worked Example

Two tuning forks at 440 Hz and 443 Hz played together.

f1 = 440f2 = 443
  1. 01f_beat = |f1 - f2|
  2. 02f_beat = |440 - 443|
  3. 03f_beat = 3 Hz
  4. 04T_beat = 1 / 3 = 0.333 s

Frequently Asked Questions

How are beats used in tuning?

A musician plays a reference tone and the instrument simultaneously. As the instrument approaches the correct pitch, the beat frequency decreases toward zero.

Can you hear beats at any frequency difference?

Beats are most clearly perceived when the frequency difference is less than about 15 Hz. Above that, the pulsation becomes too rapid to distinguish.

Do beats occur with light waves?

Yes, but light frequencies are far too high to observe beats directly. Optical heterodyne detection uses the principle electronically.

Ready to run the numbers?

Open Beat Frequency Calculator