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 of

Options

A. `117.7` cm
B. `92 .9` cm
C. `115. 5` cm
D. `113. 5` cm

Answer

a

Explanation

As, `l_(1) +x=lambda/4=22.7`
`l_(2)\+x=(3lambda)/4=70.2 and l_(3) + x (5lambda)/4`
(`therefore x=(l_(2)-3l_(1))/2=(70.2-68.1)/2=(2.1)/2=1.05 cm`
Now, `(l_(3)+x)/(l_(1)+x)=5`
`rArr l_(3)=5l_(1)+4x=5xx22.7+4xx1.05=117.7` cm