Wave Mechanics Question 1111
Question: It is desired to increase the fundamental resonance frequency in a tube which is closed at one end. This can be achieved by
[Roorkee 2000]
Options:
A) Replacing the air in the tube by hydrogen gas
B) Increasing the length of the tube
C) Decreasing the length of the tube
D) Opening the closed end of the tube
Show Answer
Answer:
Correct Answer: A
Solution:
Fundamental frequency of closed pipe $ n=\frac{v}{4l} $ where $ v=\sqrt{\frac{\gamma RT}{M}} $
Therefore $ v\propto \frac{1}{\sqrt{M}} $
$ \because $
$ {M _{H _{2}}}<M _{air},,\Rightarrow ,,{v _{H _{2}}}>v _{air} $ Hence fundamental frequency with H2 will be higher as compared to air. So option (a) is correct. Also $ n\propto \frac{1}{l} $ , hence if l decreases n increases so option (c) is correct. It is well known that (n)Open = 2(n)Closed, hence option (d) is correct.
BETA
