A massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. A block of mass $m$ is suspended from point $ O $ such that $BO$ is equal to $’x’$. Further, it is observed that the frequency of $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to $2^{nd}$ harmonic frequency in $CD$. Then, length of $BO$ is
A massless rod is suspended by two identical strings $AB$ and $CD$ of equal length. A block of mass $m$ is suspended from point $ O $ such that $BO$ is equal to $’x’$. Further, it is observed that the frequency of $1^{st}$ harmonic (fundamental frequency) in $AB$ is equal to $2^{nd}$ harmonic frequency in $CD$. Then, length of $BO$ is
- A
$\frac{L}{5}$
- B
$\frac{L}{4}$
- C
$\frac{4L}{5}$
- D
$\frac{3L}{4}$
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$(i)$ The source may be moving towards the observer with a velocity of $30\,ms^{-1}$
$(ii)$ The source may be moving towards the observer with a velocity of $33\,ms^{-1}$
$(iii)$ The observer may be moving towards the source with a velocity of $30\,ms^{-1}$
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