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. 1
• B. 4
• C. 3
• D. 2

Answer 1

The Correct Option is D

We are given three sound waves with frequencies:

• Frequency 1: \( (n-1) \)
• Frequency 2: \( n \)
• Frequency 3: \( (n+1) \)

The number of beats per second is determined by the difference in frequencies of the sound waves.

Step-by-Step Solution:

1. The difference between \( n \) and \( (n-1) \) is: 
   \(|n - (n-1)| = 1 \, \text{Hz}\)
2. The difference between \( (n+1) \) and \( n \) is: 
   \(|(n+1) - n| = 1 \, \text{Hz}\)
3. The difference between \( (n+1) \) and \( (n-1) \) is: 
   \(|(n+1) - (n-1)| = 2 \, \text{Hz}\)

The beat frequency is the difference in frequencies between the two closest sound waves:

• 1 beat per second (from \( (n-1) \) and \( n \))
• 1 beat per second (from \( n \) and \( (n+1) \))
• 2 beats per second (from \( (n-1) \) and \( (n+1) \))

Thus, the total number of beats produced per second will be:

\(1 + 1 = 2 \, \text{beats per second}\)

The correct answer is: Option 4: 2 beats per second