Two tuning forks of frequencies 256 and 258 vibrations/second are sounded together. Then the time interval between two consecutive maxima heard by an observer is

Options

A. 2 second
B. 0.5 second
C. 250 second
D. 252 second

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 1: Identify the Frequencies
Let the frequencies of the two tuning forks be:
- \( \nu_1 = 256 \, \text{Hz} \)
- \( \nu_2 = 258 \, \text{Hz} \)

### Step 2: Calculate the Beat Frequency
The beat frequency (\( f_b \)) is given by the absolute difference between the two frequencies:
\[ f_b = |\nu_1 - \nu_2| = |256 - 258| = 2 \, \text{Hz} \]

### Step 3: Determine the Time Period of the Beats
The time period (\( T \)) associated with the beat frequency is the reciprocal of the beat frequency:
\[ T = \frac{1}{f_b} = \frac{1}{2 \, \text{Hz}} = 0.5 \, \text{seconds} \]

### Conclusion
Thus, the time interval between two consecutive maxima heard by an observer is:
\[ \text{Time interval} = 0.5 \, \text{seconds} \]

### Final Answer
The correct answer is option 2: **0.5 seconds**.

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