Question

A 5.8 kg ball hangs from a steel wire 1.90 mm in diameter and 7.00 m long.

What would be the speed of a wave in the steel wire?

v=__ m/s

Answer 1

Speed of wave in steel wire will be given by:

v = sqrt(T/)

T = Tension in wire = Weight of ball = m*g

= mass per unit length

m = mass of wire = density*Volume

= density*volume/Length = rho*A*L/L = rho*pi*r^2*L/L

= rho*pi*r^2

v = sqrt(mg/(rho*pi*r^2))

r = radius of steel wire = diameter/2 = 1.90 mm/2 = 0.95 mm

rho = density of steel = 7.86*10^3 kg/m^3

v = sqrt(5.8*9.81/(pi*(0.95*10^-3)^2*7.86*10^3))

v = 50.53 m/sec

In two significant figures

v = wave speed = 51 m/sec

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