Beats occur when two waves with equal amplitude but slightly different frequencies overlap. This creates a combined wave whose amplitude wavers with a beat frequency equal to the absolute value of the difference between the original frequencies. When a tuning fork is near a piano string slightly off-tune, they produce beats that get longer as the string approaches the fork's frequency until they can no longer be heard when the frequencies match. If 7 beats occur in 3.5 seconds between a 320 Hz fork and an unknown fork, the unknown fork's frequency is 322 Hz.

1. Beats
LEARNING OBJECTIVE 8
PHYSICS 101

2.  Beats is what happens when two waves with equal amplitude but
slightly different frequencies overlap. This creates a wave of
 fav = (f1 + f2) / 2
 which amplitude wavers with frequency:
 fbeat = |f2-f1|
 These two beats with slightly different frequencies and equal
amplitudes result in something that looks like the following:

3.  A great example that demonstrates
this is when you are tuning a piano
with a tuning fork. When you listen to
the tuning fork and the piano string is
close to the tuning fork, you start to
hear some weird vibrations. As the
string and tuning fork get closer
together, the beat gets longer and
longer, eventually to the point where
you hear nothing.

4. Question
 Cindy has 2 tuning forks. One with a
frequency of 320 Hz and the other
tuning fork with an unknown frequency.
Cindy hears 7 beats in 3.5 seconds.
What is the frequency of the unknown
tuning fork.

5. Solution
 Beat Frequency is cycles over time so since Cindy hears 7 beats in 3.5 seconds, we
get 7/3.5 = 2 Hz
 Using the equation: fbeat = |f2-f1|, we can isolate f2 since we know the frequency of
the beat and the frequency of the first tuning fork.
Getting rid of the absolute value changes the fbeat to either positive or negative, so we
now have two cases, a positive and a negative beat.
+2 = f2 – 320 and -2 = f2 – 320
f2 = 318 Hz or 322 Hz.
If the second tuning fork sounded lower than the first tuning fork than it would have a
frequency of 318 Hz while if it sounded higher than the first tuning fork then it would have
a frequency of 322