Question

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

• A. $40$ cm from the open end
• B. $60$ cm from the open end
• C. $80$ cm from the open end
• D. $100$ cm from the open end

Answer 1

Answer: (B), (D)

The correct options are
B $60$ cm from the open end
D $100$ cm from the open end

For $1^{st}$ resonance $\left(1/4\right)\lambda =L$

$\Rightarrow \lambda =4L$ ..(i)

For $2$nd resonance

$3\left(\frac{\lambda }{4}\right)=L_2\Rightarrow \lambda =\frac{4L_2}{3}$ .(ii)

By using (i) and (ii)

$\frac{4L_2}{3}=4L_1$

$\Rightarrow L_2=3L_1=3\left(20\right)=60$cm

Similarly, $L_3=5L_1=100$ cm

Hence (B) and (D) are correct.