Pipe A is 0.50 m long and open at both ends. Pipe B is open at one end and closed at the other end. Determine the length of pipe B so that it has the same fundamental frequency as A.

Options

A. 0.25 m
B. 0.75 m
C. 0.50 m
D. 1.0m

Answer

To determine the length of pipe B so that it has the same fundamental frequency as pipe A, we can follow these steps:

### Step 1: Understand the properties of the pipes
- **Pipe A** is open at both ends and has a length of 0.50 m.
- **Pipe B** is open at one end and closed at the other end. We need to find its length.

### Step 2: Determine the wavelength for Pipe A
For a pipe open at both ends, the fundamental frequency corresponds to a wavelength (λ) that fits the length of the pipe. The relationship is given by:
\[ L_A = \frac{\lambda}{2} \]
Where \( L_A \) is the length of pipe A.

Given that \( L_A = 0.50 \, \text{m} \):
\[ 0.50 = \frac{\lambda}{2} \]
Thus, we can solve for λ:
\[ \lambda = 2 \times 0.50 = 1.00 \, \text{m} \]

### Step 3: Determine the wavelength for Pipe B
For a pipe closed at one end, the fundamental frequency corresponds to a wavelength that fits the length of the pipe according to the formula:
\[ L_B = \frac{\lambda}{4} \]
Where \( L_B \) is the length of pipe B.

Since we have already found that \( \lambda = 1.00 \, \text{m} \), we can substitute this value into the equation for Pipe B:
\[ L_B = \frac{1.00}{4} \]
\[ L_B = 0.25 \, \text{m} \]

### Step 4: Conclusion
The length of pipe B, so that it has the same fundamental frequency as pipe A, is:
\[ L_B = 0.25 \, \text{m} \]

### Final Answer
The length of pipe B is **0.25 m**.

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