A steel wire with mass per unit length $7.0 \times 10^{-3} \mathrm{~kg} \mathrm{m}^{-1}$ is under tension of 70 N. The speed of transverse waves in the wire will be:

(B) $100 \mathrm{~m} / \mathrm{s}$

(A) $200 \pi \mathrm{~m} / \mathrm{s}$

(C) $10 \mathrm{~m} / \mathrm{s}$

(D) $50 \mathrm{~m} / \mathrm{s}$

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Waves & Sound

A steel wire with mass per unit length

7.0 \times 1 0^{- 3} kg m^{- 1}

is under tension of 70 N. The speed of transverse waves in the wire will be:

Answer: (B)

The speed of a transverse wave on a stretched wire is

v = \frac{T}{μ}

, with

T

the tension and

μ

the mass per unit length. Substituting

T = 70 N

and

μ = 7.0 \times 1 0^{- 3} kg m^{- 1}

v = \frac{70}{7.0 \times 1 0 ^{- 3}} = 1 0^{4} = 100 m s^{- 1} .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option