A tuning fork of frequency 340 Hz is kept vibrating above a measuring cylinder of height 100 cm. Water is slowly poured in the cylinder . What is the minimum height of water in the tube for which resonance will be obtained ?
(Speed of sound in air = 340 m/s)

Options

A. 25 cm
B. 40 cm
C. 50 cm
D. 60 cm

Answer

A

Explanation

`:' v = n lambda :. lambda = v/n = 340/340 = 1 m = 100 ` cm
Let `l_(1), l_(2) " and " l_(3)` be the resonating lengths of the air columns.
Then for the first resonance , the length of the air column is , `l_(1) = lambda/4 = 100/4 = 25` cm
For second resonance, `l_(2)= (3 lambda)/4 = 75` cm
For the third resonance , `l_(3) = (5 lambda)/4 = 125` cm
[ For the tube closed at one end, only odd harmonics are produced.]
Third resonance is not possible becasue the tube length = 100 cm
` :. ` Minimum height of water of water `(h_(1)) = 100 - 75 = 25` cm
[When `h_(1) = 25 cm, ` the length of the resonating air column = 75 cm ]
For` h_(2) = 75` cm, length of the air column = 25 cm.