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 \( l_2 \) for the first and second harmonics. The difference between these lengths equals half the wavelength: \[l_2 - l_1 = \frac{\lambda}{2}\]Given \( l_1 = 100 \, \text{cm} \) and \( l_2 = 140 \, \text{cm} \), the wavelength is calculated as: \[\lambda = 2 \times (140 - 100) = 80 \, \text{cm} = 0.8 \, \text{m}\]The velocity of sound is determined using the formula: \[v = f \times \lambda\]With a frequency \( f = 400 \, \text{Hz} \) and wavelength \( \lambda = 0.8 \, \text{m} \), the velocity is: \[v = 400 \times 0.8 = 320 \, \text{m/s}\]Consequently, the velocity of sound is \( 320 \, \text{m/s} \).