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.
Given: The length of the steel wire is 12 m , the mass of the steel wire is 2.10 kg and the speed of the transverse wave on the wire is 343 m / s .
The linear mass density of the steel wire is given as,
μ = m l
Where, m is the mass of steel wire and l is the length of it.
By substituting the given values in the above equation, we get
μ = 2.10 12.0 = 0.175 kg/m
The velocity of the transverse wave on the wire is given as,
v = T μ T = v 2 μ
Where, T is the tension in the wire and v is the velocity of the transverse wave.
By substituting the given values in the above equation, we get
T = ( 343 ) 2 ( 0.175 ) = 2.06 × 10 4 N
Thus, the tension in the steel wire is 2.06 × 10 4 N .
Given: The length of the steel wire is
The linear mass density of the steel wire is given as,
Where,
By substituting the given values in the above equation, we get
The velocity of the transverse wave on the wire is given as,
Where,
By substituting the given values in the above equation, we get
Thus, the tension in the steel wire is
