QJEEM21Ph9b27: JEE Main 2021 Physics - Class 11 JEEM21Ph9b27 Solution: A closed organ pipe of length L and an open organ pipe contain…

First overtone of open pipe $= {{{v_2}} \over {{L_2}}}$

First overtone of closed pipe at one end $= {{3v} \over {4L}}$

As per question,

${{3V} \over {4L}} = {{{V_2}} \over L}$

$\Rightarrow \sqrt {{B \over {{\rho _1}}}} \,.\,{3 \over {4L}} = \sqrt {{B \over {{\rho _2}}}} \,.\,{1 \over {{L_2}}}$ ( $\because$ $V = \sqrt {{B \over \rho }}$ )

$\Rightarrow {L_2} = {{4L} \over 3}\sqrt {{{{\rho _1}} \over {{\rho _2}}}}$ ..... (i)

According to question, the length of the open pipe is

${x \over 3}L\sqrt {{{{\rho _1}} \over {{\rho _2}}}}$ ..... (ii)

Comparing Eqs. (i) and (ii), we get

$x = 4$