**Constructive interference** occurs when two waves combine to create a larger wave. This occurs when the peaks of two waves line up. **Destructive interference** occurs when two waves combine and cancel each other out. This occurs when a peak in one wave lines up with a trough in the other wave. When waves of two different frequencies interfere, a phenomenon known as *beating* occurs. The frequency of a beat is the difference of the two frequencies.

\begin{align*}f_{\text{beat}} = |f_1 -f_2|\end{align*} ; two interfering waves create a beat wave with frequency equal to the difference in their frequencies

#### Example

You want to find out the frequency of a tuning fork. When you strike the unknown fork and a fork which is known to create a sound at 100 Hz at the same time, you hear a beat frequency of 3 Hz. You strike the unknown fork a second time, but this time with a tuning fork rated for 105 Hz and you hear a beat frequency of 2 Hz. What is the frequency of the unknown fork?

Each test gives us two possibilities for a frequency. Based on the first test, the unknown fork could either be rated for 97 Hz or 103 Hz. Based on the second test, the frequency of the unknown fork could either be 103 Hz or 107 Hz. The two tests agree on 103 Hz, so that must be the frequency of the unknown tuning fork.

### Review

- At the Sunday drum circle in Golden Gate Park, an Indian princess is striking her drum at a frequency of 2 Hz. You would like to hit your drum at another frequency, so that the sound of your drum and the sound of her drum “beat” together at a frequency of 0.1 Hz. What frequencies could you choose?
- You and your friend play the same note. Your friend's instrument is in tune and is playing a note at 256 Hz, but you are slightly out of tune and are playing a note at 258 Hz. What is the beat frequency?

**Review (Answers)**

- 1.9 Hz or 2.1 Hz
- 2 Hz