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) $200 cm$
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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. } $
