A glass tube is open at both the ends. A tuning fork of
frequency f resonates with the air column inside the
tude. Now, the tube is placed bertically inside water
so that half the length of the tube is filled with water.
Now, the air column inside the tube is in unison with
another fork of frequency f . Then

Options

A. `f' = f`
B. `f' = 4f`
C. `f' = 2f`
D. `f' = f/2`

Answer

a

Explanation

For fundamental frequency of vibration of air column
`l=lambda/ 2 rArr lambda=2l`
Frequency, `f=v/lambda rArr f=v/(2l)` …(i)
When tube is placed inside water with half length
immersed in water, then

`l=lambda/2 ` `/2=lambda_(2)/4`
`l/2=lambda/4 rArr lambda'=2l`
Frequency `f'=v/(lambda')=v/(2l)` ...(ii)
From Eqs. (i) and (ii) we get `f'=f`