### Waves - Result Question 40

#### 42. An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50 cm$. The next larger length of the column resonating with the same tuning fork is :

[2016]

(a) $66.7 cm$

(b) $100 cm$

(c) $150 cm$

(d) $200 cm$

## Show Answer

#### Answer:

Correct Answer: 42. (c)

Solution:

- (c) For a closed organ pipe first minimum resonating length

$L_1=\frac{\lambda}{4}=50 cm$

$\therefore \quad$ Next or second resonating length, $L_2$

$\Rightarrow \frac{3 \lambda}{4}=150 cm$

If an open pipe is half submerged in water, it will become a closed organ pipe of length half that of a open pipe. It’s fundamental frequency will become

$ n^{\prime}=\frac{V}{4(\frac{\ell}{2})}=\frac{V}{2 \ell} \text{ equal to that of open pipe. } $