How Many Beats Are Heard When Three Tuning Forks Are Sounded Together?

[Amith2006]

Sir,
Three tuning forks of frequencies 100Hz,101Hz and 102Hz are sounded together. How many beats will be heard in one second?
If 2 forks are sounded together then the number of beats heard will be equal to the difference of their frequencies. But I don't know how to calculate the beat frequency if 3 forks are sounded together.

 

[Andrew Mason]

Sir,
Three tuning forks of frequencies 100Hz,101Hz and 102Hz are sounded together. How many beats will be heard in one second?
If 2 forks are sounded together then the number of beats heard will be equal to the difference of their frequencies. But I don't know how to calculate the beat frequency if 3 forks are sounded together.

If you sound the 100 together with the 102, you will get a beat frequency of 2 beats/sec on a frequency of 101 Hz. When the 101 Hz is sounded there are no further beats added. So I would say, 2 beats.

It is a little more complicated to analyse it by sounding the 100 and 101 first and then adding the 102. But if you pair 100 and 101, you get a 100.5 frequency and with 101 and 102 you get 101.5, each with one beat/sec. These two then beat down to 101 with another beat/sec. The beat frequency ends up 2/sec.

AM

 

[mukundpa]

One beat period is the interval from minimum to minimum (or maximum to maximum) intensity.

For superposition of waves of frequencies 100 Hz and 101 Hz it is 1 s.
For superposition of waves of frequencies 101 Hz and 102 Hz it is 1 s, and
For superposition of waves of frequencies 100 Hz and 102 Hz it is 0.5 s.

0.5 s after a minimum due to all three, first two combinations gives maximum intensity and hence the next minimum intensity will occur only after 1 s and hence the beat period is 1s and beat frequency will be 1 Hz.

(Draw the time intensity graph for all three combinations separately that will make the things clear)

 

[Andrew Mason]

For superposition of waves of frequencies 100 Hz and 101 Hz it is 1 s.
For superposition of waves of frequencies 101 Hz and 102 Hz it is 1 s, and
For superposition of waves of frequencies 100 Hz and 102 Hz it is 0.5 s.

0.5 s after a minimum due to all three, first two combinations gives maximum intensity and hence the next minimum intensity will occur only after 1 s and hence the beat period is 1s and beat frequency will be 1 Hz.

Please explain. Are you saying that beats from 100 + 101 will be synchronous with the beats from 101 and 102? Why?

AM