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Standard XII

Physics

Wave Speed expression

Two stretched...

Question

Two stretched strings have lengths $l$ and $2 l$ while tensions are $T$ and $4 T$ respectively: If they are made of same material the ratio of their frequencies is

2 : 1

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1 : 2

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1 : 1

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1 : 4

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Solution

The correct option is C $1 : 1$
Frequency, $ν = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$ where $μ$ is mass per unit length
$⟹$ $ν \propto \frac{\sqrt{T}}{L}$
Thus, $\frac{ν_{1}}{ν_{2}} = \frac{\sqrt{T_{1}}}{L_{1}} . \frac{L_{2}}{\sqrt{T_{2}}}$

We get $\frac{ν_{1}}{ν_{2}} = \frac{\sqrt{T}}{l} . \frac{2 l}{\sqrt{4 T}} = 1$
$⟹$ $ν_{1} : ν_{2} = 1 : 1$

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