Two unknown frequency tuning forks are used in resonance column apparatus. When only first tuning fork is excited the `1^(st)` and `2^(nd)` resonating lengths noted are `10 cm` and `30 cm` respectively. When only second tuning fork is excited `1^(st)` and `2^(nd)` resonating lengths noted are `30 cm` and `90 cm` respectively. The ratio of the frequency of the `1^(st)` to `2^(nd)` tuning fork is.

Options

A. `1 : 3`
B. `1 : 2`
C. `3 : 1`
D. `2 : 1`

Answer

C

Explanation

`f = v/lamda`
Now, `l_1 = lambda/4,l_2=(3lambda)/4`
`rArr l_2 - l_1 =lambda/2`
or `lambda = 2 (l_2-l_1)`
Substituting in Eq. (i), we have
`f = v/(2(l_2-l_1)`
`rArr f prop1/(l_2-l_1)`
`:. (f_1)/(f_2)= (l'_2-l'_1)/(l_2-l_1)=(90-30)/(30-10)=3/1`.