# Beats

## Beats

Beats occur when two waves of nearby frequencies overlap and create a new resultant wave. A wave not only travels in space but it also propagates through time, so if the two waves can produce interference by overlapping in space they should also produce an interference pattern when they overlap in time, this phenomenon is called beats.

Beats Definition: When two objects vibrate with different frequencies, you hear a fluctuating sound soft and loud sound alternatively. This phenomenon is known as beats or beats frequency of sound. The loud sound is caused by the constructive interference and the soft sound is caused by the destructive interference.

An important occurrence of the interference of waves is in the phenomenon of beats. In the simplest case, beats result when two sinusoidal sound waves of equal amplitude and very nearly equal frequencies mix. The frequency of the resulting sound (F) would be the average of the two original frequencies f₁ and f₂.

$$F = \frac{f_{1}+f_{2}}{2}$$.

The amplitude or intensity of the combined signal would rise and fall at a rate (fb) equal to the difference between the two original frequencies,

fb = f₁ – f₂

Where,

f₁ is greater than f₂.

Beats are useful in tuning musical instruments to each other: the farther the instruments are out of tune, the faster the beats. Other types of beats are also of interest. Second-order beats occur between the two notes of a mistuned octave, and binaural beats involve beating between tones presented separately to the two ears, so that they do not mix physically.

Constructive Interference: The interference is said to be a constructive interference if two waves having the same frequency meets in such a way that the crest of a wave meets the crest of another wave.

Destructive Interference: The interference is said to be a destructive interference if two waves having the same frequency meets in such a way that the crest of a wave meets the through of another wave.

Applications of Beats: The various applications of beats are: