A glass tube of length `1.0` m is completely filled with
water. A vibrating tuning fork of frequency `500` Hz is
kept over the mouth of the tube and the water is
drained out slowly at the bottom of the tube. If the
velocity of sound in air is 330 `ms^(-1)`, then the total
number of resonances that occur will be

Options

A. 2
B. 3
C. 1
D. 5

Answer

D

Explanation

`lambda=(330)/(500)=0.66m=66cm`
This tube is closed at one end. The lengths of the tube resonating are
`(lambda)/(4),(3lambda)/(4),(5lambda)/(4),(7lambda)/(4)` and so on
`(lambda)/(4)=16.5cm,(3lambda)/(4)=49.5cm,(5lambda)/(4)=82.5cm,(7lambda)/(4)=115.5cm`
But the `7^(th)` harmonic needs a length greater than the tube length `therefore` There will be three resonances as the length of the tube is only one metre.