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 $320 \, \text{m/s}$.