Two tuning forks of frequencies `256 Hz` and `258 Hz` are sounded together. The time interval, between two consecutive maxima heard by an observer is

Options

A. `0.5 s`
B. `2 s`
C. `250 s`
D. `252 s`

Explanation

To solve the problem of finding the time interval between two consecutive maxima heard by an observer when two tuning forks of frequencies 256 Hz and 258 Hz are sounded together, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Frequencies**:
We have two tuning forks with frequencies:
- \( f_1 = 256 \, \text{Hz} \)
- \( f_2 = 258 \, \text{Hz} \)

2. **Calculate the Beat Frequency**:
The beat frequency is given by the absolute difference between the two frequencies:
\[ f_{\text{beat}} = |f_2 - f_1| = |258 \, \text{Hz} - 256 \, \text{Hz}| = 2 \, \text{Hz} \]

3. **Determine the Time Period of the Beats**:
The time period \( T \) of the beats can be calculated using the formula:
\[ T = \frac{1}{f_{\text{beat}}} \]
Substituting the beat frequency:
\[ T = \frac{1}{2 \, \text{Hz}} = 0.5 \, \text{seconds} \]

4. **Conclusion**:
The time interval between two consecutive maxima heard by the observer is \( 0.5 \, \text{seconds} \).

### Final Answer:
The time interval between two consecutive maxima is **0.5 seconds**.

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