Wave Motion 2 Question 26

26. A cylindrical tube, open at both ends, has a fundamental frequency $f$ in air. The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now

(1981, 2M)

(a) $f / 2$

(b) $3 f / 4$

(c) $f$

(d) $2 f$

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Answer:

Correct Answer: 26. (c)

Solution:

  1. Initially the tube was open at both ends and then it is closed.

$$ f _o=\frac{v}{2 l _o} \text { and } f _c=\frac{v}{4 l _c} $$

Since, tube is half dipped in water, $l _c=\frac{l _o}{2}$

$$ \therefore \quad f _c=\frac{v}{4\left(\frac{l _o}{2}\right)}=\frac{v}{2 l _o}=f _o=f $$



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