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