NEET Physics Wave Mechanics NEET PYQ-Wave Mechanics

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is                                       [NEET 2015]

A) 80 cm

B) 100 cm

C)      120 cm

D) 140 cm

Correct Answer: C

Solution :

The fundamental frequencies of closed and open organ pipe are given as

\[{{v}_{c}}=\frac{v}{4l}\]

\[{{v}_{o}}=\frac{v}{2l'}\]

Given the second overtone (i.e., third harmonic) of open pipe is equal to the fundametal frequency of closed pipe

i.e., \[3{{v}_{o}}={{v}_{c}}\]

\[\Rightarrow \] \[3\frac{v}{2l'}=\frac{v}{4l}\]

\[\Rightarrow \] \[1'=6l=6\times 20=120cm\]