Waves

JEE Main level, single correct, medium

17 of 142

Question 17 of 142

A transverse wave travels on a taut steel wire with a velocity of vv when tension in it is 2.06×104N.2.06\times {10}^{4}N. When the tension is changed to T,T, the velocity changed to v2.\dfrac{v}{2}. The value of TT is close to:

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Answer: (B) 5.15×103N5.15\times {10}^{3} N

v∝Tv\propto \sqrt{T}
⇒v1v2=T1T2⇒v(v2)=2.06×104T\Rightarrow \dfrac{{v}_{1}}{{v}_{2}}=\sqrt{\dfrac{{T}_{1}}{{T}_{2}}}\Rightarrow \dfrac{v}{\left(\dfrac{v}{2}\right)}=\sqrt{\dfrac{2.06\times {10}^{4}}{T}}
⇒T=2.06×1044N=0.515×104N\Rightarrow T=\dfrac{2.06\times {10}^{4}}{4}N=0.515\times {10}^{4}N

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