question_answer

A cylindrical tube closed at one end contains air. It produces the fundamental note of frequency 512 Hz. If the tube is opened at both ends, the fundamental frequency that can be excited is

A)  256 Hz        

B)  512 Hz

C)  1024 Hz       

D)  128 Hz

Correct Answer: C

Solution :

 Let\[l\]be the length of pipe,\[v\]the speed of sound, then the fundamental tone or first harmonic of closed tube \[{{n}_{1}}=\frac{v}{4l}\] For open tube \[{{n}_{2}}=\frac{v}{2l}\] \[\therefore \] \[{{n}_{2}}=2{{n}_{1}}\] Given,         \[{{n}_{1}}=512\text{ }Hz,\] \[\therefore \] \[{{n}_{2}}=2\times 512=1024\text{ }Hz\]