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: 1
• B: 4
• C: 3
• D: 2

The phenomenon of beats occurs when two sound waves of slightly different frequencies interfere with each other. In this case, we have three sound waves with frequencies of n-1, n, and n+1.

Calculating the Beat Frequency

To find the number of beats produced per second, we focus on the two closest frequencies, which are n-1 and n. The beat frequency is determined by the difference between these two frequencies:

• Frequency of first wave: n-1
• Frequency of second wave: n
• Beat frequency: |(n) - (n-1)| = 1

Similarly, we can calculate the beat frequency between n and n+1:

• Frequency of third wave: n+1
• Beat frequency: |(n+1) - (n)| = 1

Total Beats

Since both pairs of waves produce 1 beat per second, the total number of beats produced is simply the sum of the individual beat frequencies:

• From n-1 and n: 1 beat
• From n and n+1: 1 beat

Thus, the total number of beats per second is:

1 + 1 = 2

Final Answer

The correct option is D: 2.