What should be minimum length of an open organ pipe for producing a note of 110 Hz. The speed of sound is `330 ms^(-1)`.

Explanation

To find the minimum length of an open organ pipe that produces a note of 110 Hz, we can follow these steps:

### Step 1: Understand the relationship between frequency, wavelength, and speed of sound.
The speed of sound in air (v) is related to the frequency (f) and wavelength (λ) by the formula:
\[ v = f \cdot \lambda \]

### Step 2: Rearrange the formula to find the wavelength.
We can rearrange the formula to find the wavelength:
\[ \lambda = \frac{v}{f} \]

### Step 3: Substitute the known values into the equation.
Given:
- Speed of sound, \( v = 330 \, \text{m/s} \)
- Frequency, \( f = 110 \, \text{Hz} \)

Substituting these values into the equation:
\[ \lambda = \frac{330 \, \text{m/s}}{110 \, \text{Hz}} \]

### Step 4: Calculate the wavelength.
Now, perform the calculation:
\[ \lambda = 3 \, \text{m} \]

### Step 5: Relate the wavelength to the length of the organ pipe.
For an open organ pipe, the fundamental frequency corresponds to a standing wave pattern that has one node at one end and one antinode at the other. The length of the pipe (L) is related to the wavelength by:
\[ L = \frac{\lambda}{4} \]

### Step 6: Substitute the wavelength into the length formula.
Now, substitute the calculated wavelength into the length formula:
\[ L = \frac{3 \, \text{m}}{4} \]

### Step 7: Calculate the length of the organ pipe.
Perform the calculation:
\[ L = 0.75 \, \text{m} \]

### Conclusion:
The minimum length of the open organ pipe required to produce a note of 110 Hz is **0.75 meters**.

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