The maximum length of a closed pipe that would produce a just audible sound is `(V_("sound") =336 m//s)` :-

Options

A. 4.2 cm
B. 4.2 m
C. 4.2 mm
D. 1.0 cm

Explanation

To find the maximum length of a closed pipe that would produce a just audible sound, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the maximum length of a closed pipe that can produce a sound that is just audible. The speed of sound in air is given as \( V_{\text{sound}} = 336 \, \text{m/s} \), and the lowest frequency of audible sound is \( f = 20 \, \text{Hz} \).

2. **Use the Formula for Closed Pipe**: The fundamental frequency of a closed pipe is given by the formula:
\[ L = \frac{V}{4f} \]
where \( L \) is the length of the pipe, \( V \) is the velocity of sound, and \( f \) is the frequency.

3. **Substitute the Values**: Now we can substitute the values into the formula:
\[ L = \frac{336 \, \text{m/s}}{4 \times 20 \, \text{Hz}} \]

4. **Calculate the Denominator**: First, calculate \( 4 \times 20 \):
\[ 4 \times 20 = 80 \]

5. **Perform the Division**: Now divide \( 336 \) by \( 80 \):
\[ L = \frac{336}{80} = 4.2 \, \text{m} \]

6. **Conclusion**: The maximum length of the closed pipe that would produce a just audible sound is \( 4.2 \, \text{m} \).

7. **Select the Correct Option**: Check the options provided in the question. The correct option corresponding to \( 4.2 \, \text{m} \) is option B.

### Final Answer:
The maximum length of the closed pipe is \( 4.2 \, \text{m} \), and the correct option is B.

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