question_answer

The speed of the sound in air is 333 m/s. The fundamental frequency of the open pipe is 333 Hz. The second overtone of the open organ pipe can be produced with a pipe of length

A)  0.5 m                   

B)  1.0m

C)  1.5m                    

D)  2.0m

Correct Answer: A

Solution :

                 For open pipe, fundamental frequency (n) is                 \[{{n}_{1}}=\frac{3v}{2l}=3{{n}_{1}}\]                             where I is length of pipe. For second overtone                 \[{{n}_{2}}=\frac{3v}{2l}=3{{n}_{1}}\] Given,   v = 333 m/s,                 \[{{n}_{1}}=333\,Hz\]                 \[\frac{3\times 333}{2l}=3\times 333\] \[\Rightarrow \]               \[l=\frac{2}{l}=0.5\,m\]