Two waves that are close in frequency, when combined, produce a beat pattern where the amplitude increases and decreases over time as heard by the human ear. Beats occur due to the interference created by two waves interacting, with the beat frequency equal to the difference between the two original frequencies. For example, two cellos slightly out of tune at 249Hz and 245Hz would produce a beat frequency of 4Hz.

1. Beats
PHYSICS 101

2. BEATS
If we listen to two waves of slightly different
frequencies we hear the amplitude increasing and
decreasing as a function of time.
This type of variation in amplitude is called a beat.

3. •The two waves shown here
in blue and red differ by a
small change in frequency.
•The effect of this frequency
difference is displayed by the
resultant wave shown in
green and appears to our
ears in the form of beats
(loud-soft-loud).

4. •However sometimes the
two waves are not close in
frequency as shown here in
black and blue.
•When this occurs, we
perceive them as separate
tones.

5. Two cellos in an orchestra are slightly out
of tune. They produce frequencies of 249
Hz and 245 Hz. What beat frequency is
heard?
Example Question

6. Solution
Since the amplitude modulations will have the
same frequency as the difference between the
two frequencies the resulting beat frequency
heard from the two cellos is 4Hz.
449Hz-445Hz=4Hz

7. Solution
Since the amplitude modulations will have the
same frequency as the difference between the
two frequencies the resulting beat frequency
heard from the two cellos is 4Hz.
449Hz-445Hz=4Hz