Question

A pipe open at both ends of length 1.5 m is dipped in water at one end such that \(2^{\text {nd }}\) overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of sound in air \(=330 \mathrm{~m} / \mathrm{s}\) ) (Neglect end correction)

• A. 1 m
• B. 0.75 m
• C. 0.5 m
• D. 0.25 m

Hint:

Once dipped, the pipe is closed at one end; its second overtone is the fifth harmonic with frequency 5v/4l.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
A pipe open at both ends becomes a closed pipe once one end is in water.
For a closed pipe of air column length \(l\), the frequencies are \(f=\dfrac{(2n+1)v}{4l}\); the 2nd overtone has \(n=2\).

Step 2: Calculation
\(330=\dfrac{5\times330}{4l}\Rightarrow l=\dfrac{5}{4}=1.25\text{ m}\)

Step 3: Immersed length
Length in water \(=1.5-1.25=0.25\text{ m}\), which is option (D).

Final Answer:
The length of the pipe inside the water is 0.25 m. \[ \boxed{\text{(D) }0.25\ \text{m}} \]