A resonance tube is \(40 cm\) long. The second resonance is heard when the tube is three - quarter full. What is the frequency of the tuning fork placed near the mouth of the tube? [Velocity of sound in air is \(334 m / s\) ]
A. \(2511 Hz\) B. \(1670 Hz\) C. \(835 Hz\) D. \(345 Hz\)
Correct Answer: A
Explanation
Length of water column \(=3 / 4\), length of air column \(\quad=1-3 / 4=1 / 4\). Since the length of the tube \(=40 cm\), length of air column \(\quad=1 / 4 \times 40 cm\) \(=10 cm\) \(=0.1 m\)or second resonance, $$ \begin{aligned} &=\frac{3 V}{4 L} \Rightarrow\left(\frac{3(334)}{4(0.1)}\right) Hz \\ & \Rightarrow 2505 Hz \end{aligned} $$
