Question

In the resonance experiment, the first resonance is heard when length of air column is $l_1$ and second resonance is heard when length of air column is $l_2.$ What should be the minimum length of the tube so that third resonance can also be heard

• A. ${2l}_2-l_1$
• B. ${2l}_1$
• C. ${5l}_1$
• D. ${7l}_1$

Answer 1

The correct option is A ${2l}_2-l_1$

$ϵ$ be end correction and $v$ is the speed then

For first resonance $l_1+ϵ=\frac{v}{4f_o}$

For second resonance $l_2+ϵ=\frac{3v}{4f_o}$

For first resonance $l_3+ϵ=\frac{5v}{4f_o}$

on solving above equation $l_3=2l_2-l_1$