The length of an open pipe is 48 cm and its fundamental frequency is 320 Hz. If one of the ends of the pipe is closed then its fundamental frequency will be- `(V = 330m//s)` –

Options

A. 160 Hz
B. 320 Hz
C. 200 Hz
D. 240 Hz

Answer

To solve the problem, we need to determine the fundamental frequency of a closed pipe based on the information given for an open pipe.

### Step-by-Step Solution:

1. **Identify the Length of the Open Pipe**:
The length of the open pipe (L) is given as 48 cm. We convert this to meters for calculations:
\[ L = 48 \, \text{cm} = 0.48 \, \text{m} \]

2. **Use the Formula for Fundamental Frequency of an Open Pipe**:
The fundamental frequency (f) of an open pipe is given by the formula:
\[ f = \frac{V}{2L} \]
where \( V \) is the speed of sound in air, which is given as \( 330 \, \text{m/s} \).

3. **Calculate the Fundamental Frequency of the Open Pipe**:
Substituting the values into the formula:
\[ f = \frac{330 \, \text{m/s}}{2 \times 0.48 \, \text{m}} = \frac{330}{0.96} \approx 343.75 \, \text{Hz} \]
However, the problem states that the fundamental frequency of the open pipe is 320 Hz. This means we will use this value for further calculations.

4. **Determine the Frequency of the Closed Pipe**:
For a closed pipe, the fundamental frequency is given by:
\[ f' = \frac{V}{4L} \]
Since we know the length of the pipe and the speed of sound, we can substitute these values:
\[ f' = \frac{330 \, \text{m/s}}{4 \times 0.48 \, \text{m}} = \frac{330}{1.92} \approx 171.88 \, \text{Hz} \]

5. **Relate the Frequencies of Open and Closed Pipes**:
The fundamental frequency of a closed pipe is half that of an open pipe:
\[ f' = \frac{f}{2} \]
Given that the frequency of the open pipe is 320 Hz:
\[ f' = \frac{320}{2} = 160 \, \text{Hz} \]

### Final Answer:
The fundamental frequency of the closed pipe will be **160 Hz**.

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