Question

A glass tube of length $1.0m$ is completely filled with water. A vibrating tuning fork of frequency $500Hz$ is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If the velocity of sound in air is $330m{s}^{-1}$, then the total number of resonances, that occur will be

• A. $2$
• B. $3$
• C. $1$
• D. $5$
• E. $4$

Answer 1

The correct option is B

$3$

Explanation for the correct option:

Step 1: Given data:

Length of glass tube, $l=1.0m$

frequency of the tuning fork, $f=500Hz$

velocity of sound in air is $v=330m{s}^{-1}$

Step 2:Finding the possible number of resonance in $1.0m$ tube.

Wavelength of sound $\lambda =\frac{v}{f}$

$$\begin{gathered} =330/500 \\ =0.66m \end{gathered}$$

The resonance lengths are

$$\begin{gathered} l_1=\lambda /4=0.165m \\ {l}_2=3\lambda /4=0.495m \\ {l}_3=5\lambda /4=0.825m \\ {l}_4=7\lambda /4=1.155m \end{gathered}$$

As$l_4$ is greater than $1m$, the allowed resonance is $3$.

Hence, option B is correct.