An open organ pipe sounds a fundamental note of frequency 330 Hz. If the speed in air is 330 m/s then the length of the pipe is nearly

Options

A. `0.25 m`
B. `0.50 m`
C. `0.75 m`
D. `2.00 m`

Answer

To solve the problem of finding the length of an open organ pipe that produces a fundamental note of frequency 330 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the fundamental note (f₀) = 330 Hz
- Speed of sound in air (v) = 330 m/s

2. **Use the Wave Equation:**
The relationship between the speed of sound (v), frequency (f), and wavelength (λ) is given by the equation:
\[ v = f \cdot \lambda \]
Rearranging this gives:
\[ \lambda = \frac{v}{f} \]

3. **Calculate the Wavelength (λ):**
Substitute the known values into the equation:
\[ \lambda = \frac{330 \, \text{m/s}}{330 \, \text{Hz}} = 1 \, \text{m} \]

4. **Determine the Length of the Pipe:**
For an open organ pipe, the length (L) of the pipe is related to the wavelength of the fundamental frequency by the formula:
\[ L = \frac{\lambda}{2} \]
Substitute the value of λ:
\[ L = \frac{1 \, \text{m}}{2} = 0.5 \, \text{m} \]

5. **Final Answer:**
The length of the pipe is nearly 0.5 meters.

### Summary:
The length of the open organ pipe is approximately 0.5 meters.

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