A cylindrical tube, open at both ends has a fundamental frequency f in air. The tube dipped vertically in water, so that half of it is in water, the fundamental frequency of the air colon is now:

Question

A cylindrical tube, open at both ends has a fundamental frequency f in air. The tube dipped vertically in water, so that half of it is in water, the fundamental frequency of the air colon is now: (A)  2 f  (B)  f  (C)  (3f/4)  (D)  (f/2)

Tardigrade Admin · Accepted Answer

When tube is dipped in water its acts like a closed end tube.
Frequency of fundamental tone in a cylindrical pipe open at both end's is

f = \frac{v}{2 l} ... (1)

where

v

is velocity of sound and

l

is length of pipe.
When half the length is dipped, it acts like a closed end tube,
with fundamental frequency

f^{'} = \frac{v}{4 l ^{'}}

Given,

l^{'} = \frac{l}{2}

∴ f^{'} = \frac{v}{4 ( \frac{l}{2} )} ... (2)

Comparing Eqs. (1) and (2), we get

f^{'} = f

Therefore, the fundamental frequency of air column is same as that for open one.

Q. A cylindrical tube, open at both ends has a fundamental frequency $f$ in air. The tube dipped vertically in water, so that half of it is in water, the fundamental frequency of the air colon is now:

$2 f$

$f$

$\frac{3 f}{4}$

$\frac{f}{2}$

Q. A cylindrical tube, open at both ends has a fundamental frequency f in air. The tube dipped vertically in water, so that half of it is in water, the fundamental frequency of the air colon is now:

2f

f

43f​

2f​

Q. A cylindrical tube, open at both ends has a fundamental frequency $f$ in air. The tube dipped vertically in water, so that half of it is in water, the fundamental frequency of the air colon is now:

$2 f$

$f$

$\frac{3 f}{4}$

$\frac{f}{2}$