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)

$l_1=18cm,f=\frac{v_1}{4l_1}$ (for second resonance )
and $f=\frac{3v_2}{4l_2}$ (for second resonance )
where, $l_2=x$
according to given situation
$\Rightarrow \frac{3v_2}{4l_2}=\frac{v_1}{4l_1}\Rightarrow l_2=3l_1\times \frac{v_2}{v_1};v=\sqrt{\frac{\gamma RT}{M}}$
$\Rightarrow x=54\times (\text{ A quantity greater than }1)$
Also $v_1<v_2$ as during summer temperature would be higher.
So, $X>$ 54