Question

A tuning fork of frequency 340 Hz is held vibrating at the open end of an empty measuring cylinder of length 100 cm. Water is then poured in slowly. What is the minimum height of water in the cylinder for which resonance will be obtained? (Given: Velocity of sound in air = 340 m/s, neglect end correction)

• A. 25 cm
• B. 75 cm
• C. 80 cm
• D. 50 cm

Hint:

In resonance tube experiments, always use \( L = \lambda/4 \) for the first resonance.

Answer 1

The Correct Option is A

Step 1: Calculate wavelength of sound.
\[ \lambda = \frac{v}{f} = \frac{340}{340} = 1 \, \text{m} = 100 \, \text{cm} \]
Step 2: Resonance condition for closed pipe.
For the first resonance in a closed pipe:
\[ L = \frac{\lambda}{4} \]
Step 3: Length of air column at resonance.
\[ L = \frac{100}{4} = 25 \, \text{cm} \]
Step 4: Finding height of water.
Total length of cylinder = 100 cm
\[ \text{Height of water} = 100 - 25 = 75 \, \text{cm} \] But minimum height of water corresponds to minimum air column length at resonance, hence
\[ \boxed{25 \, \text{cm}} \]