Waves

JEE Main level, single correct, medium

128 of 142

Question 128 of 142

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is v1\mathrm{v}_1, and that in the other string having radius of cross section R/2R / 2 is v2v_2. Then v2v1=\frac{v_2}{v_1}=

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Answer: (B) 2

v=Tμ=TfπR2v2v1=R1R2=2\begin{aligned} & v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{T}{f \pi R^2}} \\ & \frac{v_2}{v_1}=\frac{R_1}{R_2}=2\end{aligned}

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