Beats – two tones with close frequencies
PhysicsOscillations & WavesAges 16–17
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Sign in to playTwo pure tones with close frequencies f₁ and f₂ add up to produce beats: the loudness of the combined sound rises and falls regularly at the beat frequency |f₁ − f₂|. The graphs show each wave, their sum and the exact envelope, with a loudness bar that pulses with the envelope; press the speaker button to hear the two tones themselves. A tuning task asks you to adjust f₂ until the beats disappear.
Lesson: Superposition of two tones of close frequencies – beats
What it shows
When two sound waves of slightly different frequencies meet, they add at every instant. Their phase difference drifts steadily, so the waves alternate between reinforcing each other and partly cancelling, and the loudness rises and falls. This pulsation is called beats, and its frequency equals the difference |f₁ − f₂|. For equal amplitudes the sum is a wave at the average frequency (f₁ + f₂)/2 whose amplitude varies slowly, following the envelope. Musicians use beats to tune instruments: the beats slow down as two notes approach each other and vanish when they match.
How to use
Start with the 440 / 442 Hz pair and watch the loudness bar pulse twice per second while the sum graph swells and shrinks. Try 440 / 444 Hz and 440 / 450 Hz, then use the − and + buttons to change Frequency f₂ in 0.5 Hz steps. Lower Amplitude A₂ to see that the beats no longer fall to silence. Choose Zoom 20 ms on the Time axis to see single oscillations, and press Tuning task to tune by ear or by eye.
Parameters you can change
- Frequency of source 1 (f₁) 200–1000 Hz
- Frequency of source 2 (f₂) 200–1000 Hz
- Amplitude of source 1 (A₁, relative) 0–1
- Amplitude of source 2 (A₂, relative) 0–1
- Time axis Automatic (a few beat periods), 1 s window, 4 s window, Zoom 20 ms (single oscillations)
- Start with the tuning task
Questions to explore
- Two tuning forks of 256 Hz and 260 Hz sound together. How many beats do you hear each second?
- Why do the beats never fall completely silent when the two amplitudes are different?
- While tuning a guitar string against a reference note, the beats get slower. Is the string getting closer to the right note?
