Beat Frequency

Acoustic Beats

When two tones of slightly different frequencies $f_1$ and $f_2$ are played together, they alternate between constructive and destructive interference. The result is a pulsing "wah-wah" — acoustic beats.

$f_ ext{beat} = |f_1 - f_2|$

The beat frequency equals the absolute difference of the two source frequencies.

Why It Happens

The two waves periodically come in and out of phase. When aligned (phase difference = 0) their amplitudes add; half a beat period later (phase = $pi$) they cancel.

Used for Tuning

Musicians tune by beating: play two strings and listen for the pulsing. Slow the beating until it disappears — the strings are in unison.

Your Task

Implement beatFrequency(f1, f2) returning the beat frequency.

Run the code and hear the beats — two nearly-identical tones pulsing together.