Two tuning forks have frequencies 380 and 384 Hz respectively. When they are sounded together they
produce 4 beats. After hearing the maximum sound how long will it take to hear the minimum sound

Options

A. `(1)/(2)sec`
B. `(1)/(4)sec`
C. `(1)/(8)sec`
D. `(1)/(16)sec`

Answer

To solve the problem, we need to determine the time interval between the maximum sound (constructive interference) and the minimum sound (destructive interference) produced by the two tuning forks.

### Step-by-Step Solution:

1. **Identify the Frequencies:**
The frequencies of the two tuning forks are given as:
- \( f_1 = 380 \, \text{Hz} \)
- \( f_2 = 384 \, \text{Hz} \)

2. **Calculate the Beat Frequency:**
The beat frequency \( f_b \) is calculated as the absolute difference between the two frequencies:
\[ f_b = |f_2 - f_1| = |384 - 380| = 4 \, \text{Hz} \]

3. **Determine the Time Period of the Beats:**
The time period \( T_b \) corresponding to the beat frequency is the reciprocal of the beat frequency:
\[ T_b = \frac{1}{f_b} = \frac{1}{4} \, \text{seconds} \]

4. **Calculate the Time Interval Between Maximum and Minimum Sound:**
The time interval between the maximum sound (constructive interference) and the minimum sound (destructive interference) is half of the time period of the beats:
\[ \text{Time interval} = \frac{T_b}{2} = \frac{1/4}{2} = \frac{1}{8} \, \text{seconds} \]

### Final Answer:
The time it will take to hear the minimum sound after hearing the maximum sound is \( \frac{1}{8} \, \text{seconds} \).

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