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

Options

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

Answer

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

### Step-by-Step Solution:

1. **Identify the Frequencies**: We have three frequencies:
- \( f_1 = n - 1 \)
- \( f_2 = n \)
- \( f_3 = n + 1 \)

2. **Understand Beat Frequency**: The beat frequency is calculated using the formula:
\[ f_{\text{beat}} = |f_1 - f_2| \quad \text{or} \quad f_{\text{beat}} = |f_2 - f_3| \quad \text{or} \quad f_{\text{beat}} = |f_1 - f_3| \]
However, the maximum beat frequency will occur between the lowest and highest frequencies.

3. **Determine the Lowest and Highest Frequencies**:
- The lowest frequency is \( f_1 = n - 1 \)
- The highest frequency is \( f_3 = n + 1 \)

4. **Calculate the Beat Frequency**:
\[ f_{\text{beat}} = |f_3 - f_1| = |(n + 1) - (n - 1)| \]
Simplifying this:
\[ f_{\text{beat}} = |n + 1 - n + 1| = |2| = 2 \text{ Hz} \]

5. **Conclusion**: The number of beats produced per second is \( 2 \) Hz.

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

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