wave_mechanics organ_pipe_vibration_of_air_column Question 14
Question: A cylindrical tube, open at both ends, has a fundamental frequency $ f _{0} $ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is
[RPET 1999; RPMT 1998, 2000; J & K CET 2000; KCET 2002; BHU 2002; BCECE 2003]
Options:
A) $ 3f _{0}/4 $
B) $ f _{0} $
C) $ f _{0}/2 $
D) $ 2f _{0} $
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Answer:
Correct Answer: B
Solution:
$ {n _{\text{open}}}=\frac{v}{2{l _{\text{open}}}} $
$ {n _{\text{closed}}}=\frac{v}{4{l _{\text{closed}}}}=\frac{v}{4{l _{\text{open}}}/2}=\frac{v}{2{l _{\text{open}}}} $
$ ( As\ l _{closed}=\frac{l _{open}}{2} ) $ , i.e.
frequency remains unchanged.
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