question_answer

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 it is in water. The fundamental frequency of the air column is now:

A) \[\frac{f}{2}\]                                   

B) \[\frac{3f}{4}\]

C) \[f\]                                      

D) \[2f\]

Correct Answer: C

Solution :

                When length of open tube is\[l,\]then fundamental frequency                 \[n=\frac{v}{\lambda }=\frac{v}{2l}\] When dipped in water,                 \[n=\frac{v}{\lambda }\] Given,     \[\frac{l}{2}=\frac{\lambda }{4}\] \[\therefore \]  \[n=\frac{v}{2l}=n\] Given,      \[n=f\] \[\therefore \]     \[n=f\]