Question

In a resonance column, first and second resonance are obtained at depths 22.7 cm and 70.2 cm. The third resonance will be obtained at a depth:

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

Answer 1

The correct option is A $117.7cm$

In resonance column,

first resonance occurs at

$l_1+x=\frac{\lambda }{4}$.... (1)

Second resonance occurs at

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

From Eq. (1) and (2), we get

$l_2+x=3(l_1+x)$

Thus $x=\frac{3l_1-l_2}{2}=\frac{3\times 22.7-70.2}{2}=1.05$ cm.

Third resonance occurs at

$l_3+x=\frac{5\lambda }{4}$.

$l_3=\frac{5\lambda }{4}-x=5(l_1+x)-x=5l_1+4x=5\times 22.7+4\times 1.05=117.7cm$