Question

When open pipe is closed from one end then third overtone of closed pipe is higher in frequency by 150Hz than second overtone of open pipe. The fundamental frequency of open end pipe will be (Neglect end correction)

• A. \(75 \text{Hz}\)
• B. \(150 \text{Hz}\)
• C. \(225 \text{Hz}\)
• D. \(300 \text{Hz}\)

Hint:

Compare frequencies of the same pipe length, open and closed.

Answer 1

The Correct Option is D

Step 1: Open pipe
Let the fundamental of the open pipe be \(n_0 = \frac{v}{2L}\). Its second overtone is \(3n_0\).

Step 2: Closed pipe
Closing one end gives fundamental \(\frac{v}{4L} = \frac{n_0}{2}\). The third overtone is the \(7^{th}\) harmonic: \(7\times\frac{n_0}{2}\).

Step 3: Equation
\(\frac{7n_0}{2} - 3n_0 = 150\), so \(\frac{n_0}{2} = 150\) and \(n_0 = 300\ \text{Hz}\). Option (D).

Final Answer:
The fundamental of the open pipe is 300 Hz. \[ \boxed{\text{(D)}\ 300\ \text{Hz}} \]