Question

In a resonance column, the first and second resonance are obtained at depths 22.7 cm and 70.2 cm respectively, the third resonance will be obtained at a depth of

• A. 117.7 cm
• B. 92.9 cm
• C. 115.5 cm
• D. 113.5 cm

Answer 1

The correct option is A 117.7 cm

We have:

$l_1+e=\frac{\lambda }{4}$

$l_2+e=\frac{3\lambda }{4}$

$l_3+e=\frac{5\lambda }{4}$

Thus we get:
$l_2-l_1=l_3-l_2=\frac{\lambda }{2}=70.2-20.7=47.5$

Thus, $l_3=70.2+47.5=117.7cm$