Question

While performing a resonance column experiment to measure the speed of sound, a student gets the first resonance condition at a column length of $18cm$ during winter. Repeating the same experiment during summer, she measures the column length to be $xcm$ for the second resonance. Then

• A. $18>x$
• B. $x>54$
• C. $54>x>36$
• D. $36>x>18$

Answer 1

Answer: (B)

$l_{1}=18cm,f=\frac{v_{1}}{4 l_{1}}$ (for second resonance )
and $f=\frac{3 v_{2}}{4 l_{2}}$ (for second resonance )
where, $l_{2}=x$
according to given situation
$\Rightarrow \frac{3 v_{2}}{4 l_{2}}=\frac{v_{1}}{4 l_{1}}\Rightarrow l_{2}=3l_{1}\times \frac{v_{2}}{v_{1}};v=\sqrt{\frac{\gamma R T}{M}}$
$\Rightarrow x=54\times \left(\right.\text{ A quantity greater than }1\left.\right)$
Also $v_{1} < v_{2}$ as during summer temperature would be higher.
So, $X>$ 54