JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Waves & Sound

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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

v_{2}

. Then

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

(A) $2$
(B)2✓ Correct
(C)8
(D)4

Answer: (B)

Solution

The speed of a transverse wave on a string is

v = \frac{T}{μ}

, and for a circular cross-section

μ = ρ π r^{2}

, so

v = \frac{T}{ρ π r ^{2}} \propto \frac{1}{r}

at fixed tension and material. Therefore

\frac{v _{2}}{v _{1}} = \frac{r _{1}}{r _{2}} = \frac{R}{R /2}

. The ratio

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

2

JEE Main · 2025 · 08 Apr 2025 · Shift 2 · Single correct option

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