A steel cable has a cross-sectional area 4.49 * 10^-3 m^2 and is kept under a tension of 2.96 * 10^4 N. The density of steel is 7860 kg/m^3. Note that this value is not the linear density of the cable. At what speed does a transverse wave move along the cable?

The transverse wave will travel with a speed of 25.5 m/s along the cable.

Explanation:

let T = 2.96*10^4 N be the tension in in the steel cable, ρ = 7860 kg/m^3 is the density of the steel and A = 4.49*10^-3 m^2 be the cross-sectional area of the cable.

then, if V is the volume of the cable:

ρ = m/V

m = ρ*V

but V = A*L, where L is the length of the cable.

m = ρ * (A*L)

m/L = ρ*A

then the speed of the wave in the cable is given by:

v = √ (T*L/m)

= √ (T/A*ρ)

= √[2.96*10^4 / (4.49*10^-3*7860) ]

= 25.5 m/s

Therefore, the transverse wave will travel with a speed of 25.5 m/s along the cable.