question_answer

Fundamental frequency of an open pipe is \[{{f}_{0}},\]Fundamental frequency when it is half filled with water is

A)  \[{{f}_{0}}\]                                      

B) \[{{f}_{0}}/2\]

C)  \[2{{f}_{0}}\]                                    

D)        \[3{{f}_{0}}\]

Correct Answer: A

Solution :

If an open pipe is half submerged in water, it will become a closed organ pipe of length half that of open pipe as shown in figure.   So,  its frequency will become,                 \[{{f}_{c}}=\frac{v}{4\left( \frac{L}{2} \right)}=\frac{v}{2L}={{f}_{o}}\] \[ie\], equal to that of open pipe\[ie\], frequency will remain unchanged.