Question

In a resonance column experiment, the first resonance is obtained when the level of the water in tube is $20cm$ from the open end. Resonance will also be obtained when the water level is at a distance of

• A. $40cm$ from the open end.
• B. $60$ cm from the open end.
• C. $80$ cm from the open end.
• D. data insufficient

Answer 1

The correct option is B $60$ cm from the open end.

Frequency of first resonance in closed pipe $\nu =\frac{v}{4L_1}$ ....(1)
where $L_1=20cm$
Frequency of next resonance in closed pipe $\nu =\frac{3v}{4L_2}$ ....(2)
Equating (1) and (2), we get
$\frac{v}{4L_1}=\frac{3v}{4L_2}$
$⟹$ $L_2=3L_1=3\times 20=60cm$