Question

An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency 415 Hz for various vibrating air columns. Which one of the following lengths is not in resonance ? (velocity of sound in air = 332 m/s) (Neglect end correction)

• A. \(20 \text{cm}\)
• B. \(40 \text{cm}\)
• C. \(60 \text{cm}\)
• D. \(100 \text{cm}\)

Hint:

A closed pipe resonates at odd multiples of a quarter wavelength.

Answer 1

The Correct Option is B

Step 1: Ratio test
Compute $\frac{l}{\lambda/4}$ for each option: $\frac{20}{20} = 1$, $\frac{40}{20} = 2$, $\frac{60}{20} = 3$, $\frac{100}{20} = 5$. A closed pipe needs an odd number.

Step 2: Result
Only $2$ is even, so 40 cm. Option (B).

Final Answer:
40 cm. \[ \boxed{\text{(B)}\ 40\ \text{cm}} \]