Wave Motion 2 Question 13
13. A student is performing the experiment of resonance column. The diameter of the column tube is $4 cm$. The frequency of the tuning fork is $512 Hz$. The air temperature is $38^{\circ} C$ in which the speed of sound is $336 m / s$. The zero of the meter scale coincides with the top end of the resonance column tube. When the first resonance occurs, the reading of the water level in the column is
(2012)
(a) $14.0 cm$
(b) $15.2 cm$
(c) $16.4 cm$
(d) $17.6 cm$
Show Answer
Answer:
Correct Answer: 13. (b)
Solution:
- With end correction,
$$ \begin{aligned} f & =n\left[\frac{v}{4(l+e)}\right], \quad(\text { where }, n=1,3, \ldots) \\ & =n\left[\frac{v}{4(l+0.6 r)}\right] \end{aligned} $$
Because, $e=0.6 r$, where $r$ is radius of pipe.
For first resonance, $n=1$
$$ \begin{aligned} & \therefore \quad f=\frac{v}{4(l+0.6 r)} \\ & \text { or } \quad l=\frac{v}{4 f}-0.6 r=\left[\left(\frac{336 \times 100}{4 \times 512}\right)-0.6 \times 2\right] cm \\ & =15.2 cm \end{aligned} $$
