### Waves - Result Question 50

#### 52. A cylindrical resonance tube open at both ends, has a fundamental frequency, ’ $f$ ’ in air. If half of the length is dipped vertically in water, the fundamental frequency of the air column will be

(a) $2 f$

(b) $3 f / 2$

(c) $f$

(d) $f / 2$ [1997]

## Show Answer

#### Answer:

Correct Answer: 52. (c)

Solution:

- (c) Fundamental frequency of open pipe, $f=\frac{v}{2 l}$

When half of tube is filled with water, then the length of air column becomes half $(l^{\prime}=\frac{l}{2})$ and the pipe becomes closed.

So, new fundamental frequency

$f^{\prime}=\frac{v}{4 l^{\prime}}=\frac{v}{4(\frac{l}{2})}=\frac{v}{2 l}$

Clearly $f^{\prime}=f$.