What is the fundamental frequency of an open organ pipe of length 42.5 cm, if the velocity of sound in air is 340 m/s?

Explanation

To find the fundamental frequency of an open organ pipe, we can follow these steps:

### Step 1: Write down the given data
- Length of the open pipe (L) = 42.5 cm = 0.425 m (conversion from cm to m)
- Velocity of sound in air (V) = 340 m/s

### Step 2: Use the formula for the fundamental frequency
The formula for the fundamental frequency (f) of an open pipe is given by:

\[ f = \frac{V}{2L} \]

### Step 3: Substitute the values into the formula
Now, substitute the values of V and L into the formula:

\[ f = \frac{340 \, \text{m/s}}{2 \times 0.425 \, \text{m}} \]

### Step 4: Calculate the denominator
Calculate \( 2L \):

\[ 2L = 2 \times 0.425 = 0.85 \, \text{m} \]

### Step 5: Calculate the frequency
Now substitute this value back into the frequency formula:

\[ f = \frac{340}{0.85} \]

### Step 6: Perform the division
Now, perform the division:

\[ f = 400 \, \text{Hz} \]

### Final Answer
The fundamental frequency of the open organ pipe is **400 Hz**.

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