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)

Question

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in water drum to half of its length. The fundamental frequency of the air column is now equal to:

Answer 1

Step 1: Frequencies in terms of L
Open pipe first overtone: $2 \cdot \dfrac{v}{2L} = \dfrac{v}{L}$. Closed pipe second overtone: $5 \cdot \dfrac{v}{4L} = \dfrac{5v}{4L}$.

Step 2: Difference
$\dfrac{5v}{4L} - \dfrac{v}{L} = \dfrac{v}{4L} = 100$ Hz.

Step 3: Fundamental
$f_0 = \dfrac{v}{2L} = 2 \times 100 = 200$ Hz. Option (A).

Final Answer:
Option (A). \[ \boxed{200 \text{ Hz}} \]

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)

Show Hint

The Correct Option is A

Solution and Explanation

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