Beats

What are beats? Why are they important? Let's see.

(By the way, it remind me of MJ's song "Beat it"!)

Let me ask a question first.

So here goes the basic idea:

• "Beats is the periodic variation between maximum and minimum $loudness$ of sound"*

They are produced due to $interference$ of two sound waves of slightly different $frequencies$.

$Note$: Beats are not recognizable if frequency difference of two sounds is more than $10 Hz$.

To calculate the number of beats of two sounds, find the difference between their frequencies.

Beats are importance because they are used to:

1. find unknown frequency

2. tune a musical instrument at a particular frequency

3. produce variety in music (one of my favourites!)

I hope you enjoyed the beats. Now, you can turn on the music and enjoy. Let's beat it!

Let us now consider a more mathematical treatment of beats.

Consider two sound waves having equal amplitude and travelling in a medium in same direction but having slightly different frequencies. The equations of the two waves are given by:

$p_{1} = p_{0}\sin \omega_{1}(t-x/v)$

$p_{2} = p_{0}\sin \omega_{2}(t-x/v)$

where $p_{0}$ is the $Pressure$ $Amplitude$ and $p_{1}$ and $p_{2}$ are pressure variations in air changing with time. Here we have chosen the two waves to be in phase at $x = 0$, $t = 0$.