Question

Three sound waves of equal amplitudes have frequencies $(n-1),n,(n+1)$. They superimpose to give beats. The number of beats produced per second will be:
A. $2$
B. $1$
C. $4$
D. $3$

Answer 1

Hint: The beat frequency or beats per second is the difference between frequencies of two notes which interfere to produce beats. Since here three frequencies are given, we can find the difference between a pair of frequencies, and then add the results.

Complete step-by-step answer:
Beats are defined as the periodic repetition of fluctuating intensities of sound waves. This occurs when two sound waves of similar frequencies interfere with one another. It is characterised by waves whose amplitude varies at a regular rate. The beats oscillate to and fro between amplitude zero and maximum amplitude.
The positive amplitude is called crest and the negative amplitude is called trough. A loud sound is heard when the waves interfere constructively. This happens when two crests or two troughs interfere. Similarly, no sound is heard when the waves interfere destructively. This happens when one crest and one trough interferes.
The beat frequency or beats per second is the difference between frequencies of two notes which interfere to produce beats.
Here since frequencies $(n-1),n,(n+1)$ superimpose to form beats, then the difference in frequency $(n-1),n$ is $1$. i.e. $n-(n-1)=n-n+1=1$
Similarly the difference in frequency $n,(n+1)$ is $1$.i.e. $n+1-n=1$
 Then the total difference between $(n-1),n,(n+1)$ is $2$.i.e $[n-(n-1)]+[n+1-n]=1+1=2$.
Hence the answer is A.$2$

Note: Beats oscillate to and fro between amplitude zero and maximum amplitude. Beats per second is the difference between frequencies. Since the given frequencies are consecutive, we can directly take the difference between the 1st and 3rd frequency $(n-1),(n+1)$ which will give $n+1-(n-1)=n+1-n+1=2$.