Introduction to the Concept of Beats

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.

When does Beats Occur?

Beats occur when two waves of nearby frequencies overlap and create a new resultant wave, to understand this phenomenon let us conduct an experiment,

We will need two tuning forks of close frequencies e.g. 700 Hz and 705 Hz

Both the frequencies are almost identical and there is no major difference in the audible frequency you hear when you play each of them individually, but when played together these two frequencies , interfere with each other, as they are very close to each other in terms of frequencies their crest-crest interference produces a constructive interference and increases the amplitude of the wave hence the loudness of sound increases. 

When a crest-trough meet the interference produced will be destructive in nature hence they both will cancel out and the amplitude produced will be equal to zero hence the loudness will reduce to zero, the frequency at which the loudness increases and decrease is known as the beat frequency, this beat frequency is equal to the difference between the two frequencies which produced it.

In our case we have frequency A as 700 Hz, frequency B as 705 Hz therefore if these two frequencies interfere in time, the resultant beat frequency will be of 705-700 Hz = 5 Hz,

This way we can find out the difference in two close frequencies by listening to their beats, the closer the two frequencies are the smaller the resultant frequency would be. Eventually, the beats would disappear.

Piano tuners use this technique of beats and interference to finely tune piano wires, they pluck the wire and a tuning fork at the same time, and then depending on the beats frequency they will tighten or loosen the wire tension to increase or reduce the frequency thereby tuning the wire to the same frequency as the fork, eventually, the beats vanish when the wire is perfectly in tune.

Activity: if we can hear beats when two close frequency are played, then why don’t we hear any beats when two piano notes are played?

Solution: Because the difference in frequencies between any two adjacent keys on a piano is more than 7 Hz and human ears cannot hear beats with frequencies more than 7 Hz.