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 secti

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Solution

Q.
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 $v_{1}$ , and that in the other string having radius of cross section R/2 is $v_{2}$ . Then $\frac{v_{2}}{v_{1}} =$ [2025]

1 $\sqrt{2}$

2 2

3 8

4 4

Ans.
(2)

$v = \sqrt{\frac{T}{μ}} = \sqrt{\frac{T}{ρ π R^{2}}}$

$\Rightarrow \frac{v_{2}}{v_{1}} = \frac{R_{1}}{R_{2}} = 2$

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