A Steel Wire Has a Length of 12.0 M and a Mass of 2.10 Kg. What Should Be the Tension in the Wire So that Speed of a Transverse Wave on the Wire Equals the Speed of Sound in Dry Air at 20 °C = 343 M S–1. - Physics

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 20 °C = 343 m s–1.

Solution 1

Length of the steel wire, l = 12 m

Mass of the steel wire, m = 2.10 kg

Velocity of the transverse wave, v = 343 m/s

Mass per unit length, mu = m/l = 2.10/12 = 0.175 kg m^(-1)

For tension T, velocity of the transverse wave can be obtained using the relation:

v = sqrt(T/mu)

:. T = v^2mu

= (343)2 × 0.175 = 20588.575 ≈ 2.06 × 104 N

Solution 2

Here l = 12.0 m, M = 2.10 kg

v = 343 "ms"^(-1)

Mass per unit length  = M/l = 2.10/12.0 = 0.175 "kg m"^(-1)

As v = sqrt(T/m)

:. T = v^2. m = (343)^2 xx 0.175 = 2.06 xx 10^(4) N

Concept: The Speed of a Travelling Wave
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NCERT Class 11 Physics
Chapter 15 Waves
Exercises | Q 3 | Page 387