Question

The end correction of a resonance column is $1cm$. If the shortest length resonating with the tuning fork is $10cm$, the next resonating length should be

• A. $32cm$
• B. $40cm$
• C. $28cm$
• D. $36cm$

Answer 1

The correct option is A $32cm$

Let the shortest resonating length be $l_1$

And the next be $l_2$

Then, $l_1+e=\frac{\lambda }{4}$ ............ (1)

$l_2+e=\frac{3\lambda }{4}$ .............(2)

Here, e = end correction

On dividing (1) by (2)

$\frac{l_1+e}{l_2+e}=\frac{1}{3}$

$\frac{10+1}{l_2+1}=\frac{1}{3}$

$33=l_2+1$

$l_2=32cm$