Two waves of frequencies 50 Hz and 45 Hz are produced simultaneously, then the time interval between successive maxima of the resulting wave is [maxima refers to the maximum intensity]

Options

A. 0.2 s
B. 0.02 s
C. 0.04 s
D. 0.4 s

Answer

To solve the problem of finding the time interval between successive maxima of the resulting wave produced by two waves of frequencies 50 Hz and 45 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
We have two frequencies given:
- \( f_1 = 50 \, \text{Hz} \)
- \( f_2 = 45 \, \text{Hz} \)

2. **Calculate the Beat Frequency**:
The beat frequency \( f_{\text{beat}} \) can be calculated using the formula:
\[ f_{\text{beat}} = |f_1 - f_2| \]
Substituting the values:
\[ f_{\text{beat}} = |50 \, \text{Hz} - 45 \, \text{Hz}| = 5 \, \text{Hz} \]

3. **Calculate the Time Period of the Beat Frequency**:
The time period \( T \) of the beat frequency can be calculated using the formula:
\[ T = \frac{1}{f_{\text{beat}}} \]
Substituting the value of the beat frequency:
\[ T = \frac{1}{5 \, \text{Hz}} = 0.2 \, \text{seconds} \]

4. **Conclusion**:
The time interval between successive maxima of the resulting wave is \( 0.2 \, \text{seconds} \).

### Final Answer:
The time interval between successive maxima of the resulting wave is **0.2 seconds**.

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