Beat frequency

AP Physics 2 EK 14.6.A.6: beats arise from the addition of two waves of slightly different frequency. EK 14.6.A.6.i gives the mechanism: waves with different frequencies are sometimes in phase and sometimes out of phase at locations along the waves, causing periodic amplitude changes in the resultant wave.

The relationship is stated at EK 14.6.A.6.ii and printed on the AP Physics 2 equation sheet:

$|f_{\text{beat}}| = |f_1 - f_2|$

Difference, not average. A 440 Hz fork and a 444 Hz fork give 4 beats per second. The pitch you hear sits near 442 Hz, which is the average, but the throbbing you count is 4 Hz, which is the difference. Those are two different questions and the exam asks the second one.

Why the absolute value is there. Order does not matter, so a beat frequency is never negative, and on its own it never tells you which source is the sharper of the two. Detuning either fork by 4 Hz in either direction produces the same 4 Hz beat.

EK 14.6.A.6.iii notes that tuning forks are the devices commonly used to demonstrate beat frequencies, which is the apparatus most exam questions describe. Zero beats means the two frequencies are equal, which is how an instrument gets tuned by ear.