question_answer

 A piston Filled in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13 cm, 41 cm and 69 cm. The frequency  of tuning fork, if velocity of sound is 350 m/s is :

A)  1250 Hz      

B)  625 Hz

C)  417 Hz       

D)  715 Hz

Correct Answer: B

Solution :

 In a closed organ pipe in which length of air-column can be increased or decreased. The first resonance occrus at \[\lambda /4\] and second resonance occurs at \[3\lambda /4\]. Thus, at first resonance \[\frac{\lambda }{4}=13\] ... (i) and at second resonance \[\frac{3\lambda }{4}=41\] ... (ii) Subtracting Eq. (i) from Eq. (ii), we have \[\frac{3\lambda }{4}-\frac{\lambda }{4}=41-13\] \[\Rightarrow \] \[\frac{\lambda }{2}=28\] \[\therefore \] \[\lambda =56\,\,cm\] Hence, frequency of tuning fork \[n=\frac{v}{\lambda }=\frac{350}{56\times {{10}^{-2}}}=625\,Hz\] Note: In resonance tube antinode is not formed exactly at open end but it is formed a little above the open end known as end correction [e]. So. in first and second state of air-column, the lengths are \[{{l}_{1}}+e\] and \[{{l}_{2}}+e\].