Three sound waves of equal amplitudes have frequencies `(v - 1), v, (v + 1)`. They superpose to give beats. The number of beats produced per second will be :

Options

A. 4
B. 3
C. 2
D. 1

Answer

To solve the problem of finding the number of beats produced per second by three sound waves with frequencies \((v - 1)\), \(v\), and \((v + 1)\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies:**
The frequencies of the three sound waves are given as:
- \(f_1 = v - 1\)
- \(f_2 = v\)
- \(f_3 = v + 1\)

2. **Calculate the Differences Between Frequencies:**
To find the number of beats, we need to calculate the differences between each pair of frequencies:
- Difference between \(f_1\) and \(f_2\):
\[ |f_1 - f_2| = |(v - 1) - v| = |-1| = 1 \]
- Difference between \(f_2\) and \(f_3\):
\[ |f_2 - f_3| = |v - (v + 1)| = |-1| = 1 \]
- Difference between \(f_1\) and \(f_3\):
\[ |f_1 - f_3| = |(v - 1) - (v + 1)| = |-2| = 2 \]

3. **Determine the Maximum Difference:**
The number of beats produced per second is determined by the maximum difference in frequency among the three waves. From our calculations:
- The differences are \(1\), \(1\), and \(2\).
- The maximum difference is \(2\).

4. **Conclusion:**
Therefore, the number of beats produced per second is equal to the maximum frequency difference, which is \(2\).

### Final Answer:
The number of beats produced per second is \(2\).

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