7.9 Beats

7.9 Beats

When two waves of slightly different frequencies, travelling in the same direction overlap each other then there is a periodic variation of sound between maximum and minimum loudness which is called as beats.

Tuning forks give out pure notes (single frequency). If two tuning forks $A$ and $B$ of the same frequency say $32\,\mathrm{Hz}$ are sounded separately, they will give out pure notes. If they are sounded simultaneously, it will be difficult to differentiate the notes of one tuning fork from that of the other. The sound waves of the two will be superposed on each other and will be heard by the human ear as a single pure note.

If the tuning fork $B$ is loaded with some wax or plasticine, its frequency will be lowered slightly, say it becomes $30\,\mathrm{Hz}$. If now the two tuning forks are sounded together, a note of alternately increasing and decreasing intensity will be heard. This note is called beat note or a beat which is due to interference between the sound waves from tuning forks $A$ and $B$.

Fig. 7.13 (a) shows the waveform of the note emitted from a tuning fork $A$. Similarly, Fig. 7.13(b) shows the waveform of the note emitted by tuning fork $B$. When both the tuning forks $A$ and $B$ are sounded together, the resultant waveform is shown in Fig. 7.12(c). It shows how do the beat note occur. At some instant $X$, the displacement of the two waves is in the same direction. The resultant displacement is large and a loud sound is heard.

After $1/4\,\mathrm{s}$ the displacement of the wave due to one tuning fork is opposite to the displacement of the wave due to the other tuning fork resulting in minimum displacement at $Y$, hence, faint sound or no sound is heard.

Another $1/4\,\mathrm{s}$ later, the displacements are again in the same direction and a loud sound is heard again at $Z$.

Thus, during one second, we observe two faintest sounds or two loudest. As the difference of the frequency of the two tuning forks is also $4\,\mathrm{Hz}$ so, we find that the number of beats per second is equal to the difference between the frequencies of the tuning forks.

$f_{A} = 32\,\mathrm{Hz}$, $f_{B} = 30\,\mathrm{Hz}$, $f_{A} > f_{B}$

However, when the difference between the frequencies of the two sounds is more than $10\,\mathrm{Hz}$, it becomes difficult to recognize the beats.

The difference between the frequencies of the two waves is termed as beat frequency $(f_{\mathrm{beat}})$.

One can use beats to tune a string instrument, such as piano or violin, by beating a note against a note of known frequency. The string can then be adjusted to the desired frequency by tightening or loosening it until no beats are heard.