Beats

When two waves with almost the same frequency are joined together, they produce another tone of different frequency, this is called as beat.

If two waves blue wave and red wave with almost the same frequecy are joined together, they form a beat represented in the third image. The purple wave represents the beat.

Beats are change in amplitude. The frequency of a beat is expressed as the equation

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

$$f_{beat}$$ is the frequency of the beat, $$f_1$$ and $$f_2$$ are the frequencies of the two given tones which is almost similar with each other.

Example 1.

A wave has a frequency of $$305\;Hz$$. Another wave has a frequency of $$300 \;Hz$$. What is the frequency of the beat produced by the two waves?

Solution:

$$f_{beat}=|f_1-f_2|=|305\;Hz – 300\;Hz|=5\;Hz$$.

The frequency of the beat is $$5\;Hz$$.

Example 2.

Belle is tuning her guitar. The first string has a frequency of $$100 \;Hz$$. She was trying to make the same tune on the second string, but heard a different tone with a frequency of $$102 \;Hz$$. Solve for the beat produced.

Solution:

$$f_{beat}=|f_1 - f_2|=|100\;Hz – 102\;Hz|=2\;Hz$$.