question_answer

A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If 1/4th of the tube is immersed vertically in water the fundamental frequency of air column is

A) 260 Hz            

B) 130 Hz

C) 390 Hz            

D) 520 Hz.

Correct Answer: A

Solution :

[a]: A cylindrical tube open at both the ends, its fundamental frequency is where v is the velocity of sound in air. \[\upsilon =\frac{v}{\lambda }=\frac{v}{2L}=390Hz\]                             (i) If a (1/4)th of cylindrical tube is immersed in a water, it will become a closed pipe of length three-fourth that of an open pipe as shown in figure (ii). Therefore, its fundamental frequency is \[\upsilon '=\frac{v}{\lambda '}=\frac{v}{3L}\] \[\upsilon '=\frac{v}{3L}=\frac{2}{3}\left( \frac{v}{2L} \right)=\frac{2}{3}\times 390Hz\](using (i)) = 260 Hz.