JEE Main 2025 Apr 8 Shift 2, Physics Q13: Types and Equations of Waves

JEE Main2025Apr 8, Shift 2Physics

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 $\frac{v _{2}}{v _{1}}$ =

A
$2$
B
$2$
C
$8$
D
$4$

Solution

Wave speed on a string is $v = T / μ$ , where $μ$ is linear mass density.

For a string of cross-sectional area $A = π r^{2}$ made of material with density $ρ$ , $μ = ρ π r^{2}$ , so $v = \frac{T}{ρ π r ^{2}} = \frac{1}{r} \frac{T}{ρ π}$ .

Since $T$ and material are the same for both strings, $v \propto \frac{1}{r}$ , so $\frac{v _{2}}{v _{1}} = \frac{r _{1}}{r _{2}} = \frac{R}{R /2} = 2$ , matching option (2).

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JEE Main 2025 Apr 8 Shift 2, Physics Q13: Types and Equations of Waves

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