Question

In a resonance tube experiment at one end, resonance is obtained at two consecutive lengths \( l_1 = 100 \, \text{cm} \) and \( l_2 = 140 \, \text{cm} \). If the frequency of the sound is 400 Hz, the velocity of sound is:

• A. 320 m/s
• B. 340 m/s
• C. 380 m/s
• D. 300 m/s

Hint:

In resonance tube experiments, the difference in tube lengths gives the wavelength, and from that, you can calculate the velocity of sound.

Answer 1

The Correct Option is B

In a resonance tube experiment, resonance occurs at two consecutive lengths \( l_1 \) and \( l_2 \) when the tube resonates at the first and second harmonics. The difference between these two lengths is half of the wavelength: \[ l_2 - l_1 = \frac{\lambda}{2} \] Given that \( l_1 = 100 \, \text{cm} \) and \( l_2 = 140 \, \text{cm} \), we find: \[ \lambda = 2 \times (140 - 100) = 80 \, \text{cm} = 0.8 \, \text{m} \] Now, we can calculate the velocity of sound using the formula: \[ v = f \times \lambda \] Where: - \( f = 400 \, \text{Hz} \) (frequency) - \( \lambda = 0.8 \, \text{m} \) (wavelength) Thus: \[ v = 400 \times 0.8 = 320 \, \text{m/s} \] Therefore, the velocity of sound is \( 320 \, \text{m/s} \).