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}.

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#### 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 × 10^{4} 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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