Wave Mechanics Question 675
Question: An open pipe is in resonance in 2nd harmonic with frequency $ f _{1} $ Now one end of the tube is closed and frequency is increased to $ f _{2} $ such that the resonance again occurs in nth harmonic. Choose the correct option
Options:
A) $ n=3,,f _{2}=\frac{3}{4}f _{1} $
B) $ n=3,,f _{2}=\frac{5}{4}f _{1} $
C) $ n=5,,f _{2}=\frac{3}{4}f _{1} $
D) $ n=5,,f _{2}=\frac{5}{4}f _{1} $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ \lambda =\ell $
$ \
Therefore f _{1}=\frac{v}{\lambda }=\frac{v}{\ell } $ ?. (i) $ \lambda =\frac{4\ell }{n} $
$ \
Therefore ,f _{2}=\frac{v}{\lambda }=\frac{nv}{4\ell } $ ?. (ii) Here n is a odd number. From (i) and (ii) $ f _{2}=\frac{n}{4}f _{1} $ For first resonance, $ n=5,,f _{2}=\frac{5}{4}f _{1} $
BETA
