The frequency of the first overtone of an open pipe is 300 Hz. What is the fundamental frequency?

Answer

To find the fundamental frequency of an open pipe when the frequency of the first overtone is given, we can follow these steps:

### Step 1: Understand the relationship between frequencies
The fundamental frequency (first harmonic) of an open pipe is denoted as \( f_1 \), and the first overtone (second harmonic) is denoted as \( f_2 \). For an open pipe, the relationship between the fundamental frequency and the first overtone is given by:
\[ f_2 = 2f_1 \]

### Step 2: Use the given information
We are given that the frequency of the first overtone \( f_2 \) is 300 Hz.

### Step 3: Set up the equation
Using the relationship established in Step 1, we can express the first overtone in terms of the fundamental frequency:
\[ f_2 = 2f_1 \]
Substituting the known value:
\[ 300 = 2f_1 \]

### Step 4: Solve for the fundamental frequency
Now, we can solve for \( f_1 \):
\[ f_1 = \frac{300}{2} \]
\[ f_1 = 150 \text{ Hz} \]

### Final Answer
The fundamental frequency of the open pipe is **150 Hz**.

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