Waves

JEE Main level, single correct, medium

69 of 142

Question 69 of 142

Two identical strings XX and ZZ made of same material have tension TX{T}_{X} and TZ{T}_{Z} in then if their fundamental frequencies are 450Hz450Hz and 300Hz300Hz, respectively, then the ratio TX/TZ{T}_{X}/{T}_{Z} is :

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Answer: (A) 2.252.25

fX=12ℓTXμ\begin{matrix}{f}_{X}=\dfrac{1}{2\ell }\sqrt{\dfrac{{T}_{X}}{\mu }}\end{matrix}
fZ=12ℓTZμ\begin{matrix}{f}_{Z}=\dfrac{1}{2\ell }\sqrt{\dfrac{{T}_{Z}}{\mu }}\end{matrix}
fXfZ=450300=TXTZ\begin{matrix}\dfrac{{f}_{X}}{{f}_{Z}}=\dfrac{450}{300}=\sqrt{\dfrac{{T}_{X}}{{T}_{Z}}} \\ \end{matrix}
⇒TX/TZ=9/4=2.25\Rightarrow {T}_{X}/{T}_{Z}=9/4=2.25

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