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

Options

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

Answer

A

Explanation

`l_1+x=lamda/4=22.7 `equation (1) ,
`l_2+x=(3 lamda)/4=70.2` (equation 2)
`l_3+x=(5 lamda)/4` (equation (3)
From equation (1) and (2)
`x=(l_2-3l_1)/2=(70.2-68.1)/2=2.1/2=1.05cm`
From equation (2) and (3) `(l_3+x)/(l_1+x)=5`
`l_3=5l_1+4x=5times22.7+4 times 1.05=117.7cm`