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. 2
B. 1
C. 4
D. 3

Answer

To find the number of beats produced per second when three sound waves of equal amplitudes with frequencies \( n-1 \), \( n \), and \( n+1 \) superimpose, we can follow these steps:

### Step-by-Step Solution:

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

2. **Determine the Maximum and Minimum Frequencies**:
Among these frequencies, the maximum frequency is \( f_3 = n + 1 \) and the minimum frequency is \( f_1 = n - 1 \).

3. **Calculate the Beat Frequency**:
The beat frequency is determined by the difference between the maximum and minimum frequencies. The formula for the number of beats per second (beat frequency) is given by:
\[ \text{Number of beats per second} = f_{\text{max}} - f_{\text{min}} \]
Substituting the values:
\[ \text{Number of beats per second} = (n + 1) - (n - 1) \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ \text{Number of beats per second} = n + 1 - n + 1 = 2 \]

5. **Conclusion**:
Therefore, the number of beats produced per second is \( 2 \).

### Final Answer:
The number of beats produced per second is **2**.

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