A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 25

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14.Waves and Sound

medium

A wire of length one metre under a certain initial tension emits a sound of fundamental frequency $256 \,Hz$. When the tension is increased by $1 \,kg$ wt, the frequency of the fundamental node increases to $320 \,Hz$. The initial tension is ........... $kg \,wt$

$3 / 4$

$4 / 3$

$16 / 9$

$20 / 9$

(c)

Let tension be $T$

$f_1=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l}=256$

$f_2=\sqrt{\frac{T+10}{\mu}} \times \frac{1}{2 l}=320$

$\sqrt{\frac{T}{T+10}}=\frac{256}{320}$

$\frac{T}{T+10}=\frac{(16)^2}{(16)^2 \times(20)^2}$

or $\frac{T}{T+10}=\frac{16^2}{(20)^2}$

or $400 T=256 T^2+2560$

or $144 T=2560$

or $T=\frac{2560}{144}$

or $T=\frac{2560}{16 \times 9}$

or $T=\frac{160}{9}$ Newton

$=\frac{16}{9} \,kg -w t$

Standard 11

Physics

easy

medium

medium

easy

easy