## Interference

It is the combination of two or more waves that are in the same region of space generating a resultant wave.

## Standing Waves

A stationary wave occurs when two or more waves, in opposite directions, form a single wave. In this wave, certain points do not move. The word "stationary" refers to these points and not to the wave as a whole, which vibrates normally out of these points. The distance between two consecutive nodes is $$\frac{\lambda}{2}$$.

This phenomenon can be observed in a rope where one of its ends is tied and the other vibrates. After traveling down the rope, the pulse is reflected back when it reaches the fixed end. The sum of the wave sent with the reflected one can generate a standing wave, depending on the characteristics of the incident wave. See the figure.

## Standing Waves in Tubes

In tubes where one end may or may not be closed, where a sound wave is applied (pressure wave in air), it is also possible to obtain standing wave so that:

Open tubes
$$f_n = \frac{nv}{2L}$$
Closed tubes
$$f_n = \frac{nv}{4L}$$

## Beats

The beat is the phenomenon that results from the superposition of two waves of slightly different frequencies. The beat is a variable amplitude perturbation whose frequency is equal to the difference between the frequencies of the two waves; that is, the number of beats per second is equal to the difference between the frequencies of the component waves: $$f_{beat} = ~ ∣f_1 - f_2∣.$$