Wave Motion 2 Question 10

10. A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water, so that half of it is in water. The fundamental frequency of the air column is now

(2016 Main)

(a) $\frac{f}{2}$

(b) $\frac{3 f}{4}$

(c) $2 f$

(d) $f$

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Answer:

Correct Answer: 10. (d)

Solution:

  1. Fundamental frequency of open pipe.

$$ f=\frac{v}{2 l} $$

Now, after half filled with water it becomes a closed pipe of length $\frac{l}{2}$.

Fundamental frequency of this closed pipe,

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



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