Beats occur when two similar sound waves are heard together. When the frequency difference is small, a single tone with a mean frequency is heard. When the difference is large, two distinct tones are heard. Beats can be visualized by combining two waves using superposition to get a resultant wave formed by adding the amplitudes of the individual waves over time.

1. BEATS
By Andrew Kim

2. What Are Beats?
• Variance in amplitude as it increases and decreases.
• Occurs when we listen to two similar waves.
• When frequencies of two waves are significantly different, we
hear to distinct tones.

3. Problem 1
a)You pluck two steel strings at once. The first string
emits 673 Hz and the second string emits 678 Hz.
What sound wave(s) do you hear?
b)You pluck two steel strings that emit 432 Hz and 490
Hz. What sound wave(s) do you hear?

4. Solution 1
a) Since the two frequencies are very close to each other, you will
hear a single tone with a mean frequency of the two waves; 675
Hz.
b) The frequency difference of the two waves are clearly large.
Therefore, you will hear two distinct tones that are 432 Hz and 490
Hz,

5. Visualizing Beats
• Two waves (blue and red) combine to
form the resultant wave (green).
• We can utilize the principle of
superposition to determine the
resultant wave; add the two waves.

6. Problem 2
Wave 1 Wave 2
A
m
p
l
i
t
u
d
e
Time
Determine the resulting wave.

7. Solution 2
Resultant
Wave
Add the amplitudes of two waves to obtain
the resultant wave.

8. References
• Physics 101 UBC Edition