A transverse wave travels on a taut steel wire with velocity of V when tension in it is $$2.06$$×$$104N$$. When the tension is changed to T. The velocity changed to $$V/2$$ the value of T is close to $$_____$$ ×$$103N$$

Velocity of transverse wave is given by v V ∝T $$v=T$$μ ⇒$$V1V2=T1T2$$ S.B.S ⇒$$V12V22=T1T2$$ ⇒$$V2V22=T1T2$$ ⇒$$T2=T14$$ ⇒$$T2=2.06$$×$$1044$$ $$=5.15$$×$$103N$$

Travelling wave

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Question

A transverse wave travels on a taut steel wire with velocity of V when tension in it is $2.06 \times 10^{4} N$ . When the tension is changed to T. The velocity changed to $V / 2$ the value of T is close to _____ $\times 10^{3} N$

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Solution

Velocity of transverse wave is given by v
$V \propto \sqrt{T} v = \sqrt{\frac{T}{μ}} \Rightarrow \frac{V_{1}}{V_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} S . B . S \Rightarrow \frac{V_{1}^{2}}{V_{2}^{2}} = \frac{T_{1}}{T_{2}} \Rightarrow \frac{V^{2}}{{(\frac{V}{2})}^{2}} = \frac{T_{1}}{T_{2}} \Rightarrow T_{2} = \frac{T_{1}}{4} \Rightarrow T_{2} = \frac{2.06 \times 10^{4}}{4} = 5.15 \times 10^{3} N$

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Travelling wave

Remember concepts with our Masterclasses.

A transverse wave travels on a taut steel wire with velocity of V when tension in it is 2.06×104N. When the tension is changed to T. The velocity changed to V/2 the value of T is close to _____ ×103N

Velocity of transverse wave is given by v V ∝T v=Tμ ⇒V1V2=T1T2 S.B.S ⇒V12V22=T1T2 ⇒V2V22=T1T2 ⇒T2=T14 ⇒T2=2.06×1044 =5.15×103N

Ready to Test Your Skills?

free study material

A transverse wave travels on a taut steel wire with velocity of V when tension in it is $2.06 \times 10^{4} N$ . When the tension is changed to T. The velocity changed to $V / 2$ the value of T is close to _____ $\times 10^{3} N$