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 $18 \, cm \, $ during winter. Repeating the same experiment during summer, she measures the column length to be $x$ cm for the second resonance. Then

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

Answer 1

Answer: (B)

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