A piston fitted 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 lengths 13 cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of

Options

A. 1250 Hz
B. 625 Hz
C. 417 Hz
D. 715 Hz

Answer

B

Explanation

In a closed organ pipe in which length of air-column can be increased or decreased, the first resonance occurs at `lambda//4` and second resonance occurs at `3lambda//4.`
Thus, at first resonance
`(lambda)/(4)=13 " " ` …(i)
and at second resonance
`(3lambda)/(4) =41 " " ` ...(ii)
Subtracting Eq. (i) from Eq. (ii), we have
`(3lambda)/(4)-(lambda)/(4)=41-13 rArr (lambda)/(2)=28`
`therefore lambda = 56 cm`
Hence, frequency of tuning fork
`n=(v)/(lambda)=(350)/(56xx10^(-2))=625Hz`