Wave Mechanics Question 1123
Question: A source of sound placed at the open end of a resonance column sends an acoustic wave of pressure amplitude $ {\rho _{0}} $ inside the tube. If the atmospheric pressure is $ {\rho _{A}}, $ then the ratio of maximum and minimum pressure at the closed end of the tube will be
[UPSEAT 2002]
Options:
A) $ \frac{({\rho _{A}}+{\rho _{0}})}{({\rho _{A}}-{\rho _{0}})} $
B) $ \frac{({\rho _{A}}+2{\rho _{0}})}{({\rho _{A}}-2{\rho _{0}})} $
C) $ \frac{{\rho _{A}}}{{\rho _{A}}} $
D) $ \frac{( {\rho _{A}}+\frac{1}{2}{\rho _{0}} )}{( {\rho _{A}}-\frac{1}{2}{\rho _{0}} )} $
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Answer:
Correct Answer: A
Solution:
Maximum pressure at closed end will be atmospheric pressure adding with acoustic wave pressure So $ {\rho _{\max }}={\rho _{A}}+{\rho _{0}} $ and $ {\rho _{\min }}={\rho _{A}}-{\rho _{0}} $ Thus $ \frac{{\rho _{\max }}}{{\rho _{\min }}}=\frac{{\rho _{A}}+{\rho _{0}}}{{\rho _{A}}-{\rho _{0}}} $
BETA
