A tuning fork of frequency 340 Hz is vibrated just above the tube of 120 cm height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance? (speed of sound in the air = 340m/s)

Options

A. 15 cm
B. 25 cm
C. 30 cm
D. 45 cm

Answer

D

Explanation

Because the tuning fork is in resonance with air column in the pipe closed at one end, the frequency is `n = ((2N-1)v)/(4l)` where N = 1,2,3 … corresponds to different mode of vibraton putting n = 340Hz, v = 340 m/s, the length of air colmn in the pipe can be
`l = ((2N -1)340)/(4 xx 340) = (2N - 1)/(4)m = ((2N -1)xx100)/(4)cm` For N = 1,2,3 ... we get l = 25cm, 75cm, 125cm .... As the tube is only 120cm long, length of air column after water is poured in it may be 25 cm or 75cm only, 125cm is not possible, the corresponding length of water column in the tube will be (120"25)cm = 95cm or (120-75)cm = 45cm.
Thus minimum length of water column is 45 cm.