Question

When open pipe is closed from one end then second overtone of closed pipe is higher in frequency by 100 Hz than first overtone of open pipe. The fundamental frequency of open end pipe will be (Neglect end correction)

• A. \(200\) Hz
• B. \(300\) Hz
• C. \(100\) Hz
• D. \(400\) Hz

Hint:

Open pipe: harmonics are f0, 2f0, 3f0. Closed pipe of the same length: odd harmonics of f0/2.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Let the open pipe of length \(L\) have fundamental \(f_0 = \dfrac{v}{2L}\). Its overtones are \(2f_0, 3f_0, \dots\), so the first overtone is \(2f_0\).

Step 2: Closed pipe
Closing one end of the same pipe gives a fundamental \(\dfrac{v}{4L} = \dfrac{f_0}{2}\). Only odd harmonics exist: \(\dfrac{f_0}{2}, \dfrac{3f_0}{2}, \dfrac{5f_0}{2}\). The second overtone is the 5th harmonic, \(\dfrac{5f_0}{2}\).

Step 3: Use the 100 Hz difference
\[ \frac{5f_0}{2} - 2f_0 = \frac{f_0}{2} = 100 \Rightarrow f_0 = 200 \text{ Hz} \]

Final Answer:
The fundamental frequency of the open pipe is 200 Hz, option (A). \[ \boxed{200 \text{ Hz}} \]