Question

A 5.8 kg ball hangs from a steel wire 1.80 mm in diameter and 5.00 m long.

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

Express your answer using two significant figures.

v=____________m/s

Answer 1

Wave speed in a wire is given by:

V = sqrt (T/)

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

T = 5.8*9.8 = 56.84 N

= mass per unit length of wire = m/L

Given that length of wire = 5.00 m

Cross-sectional area of wire = A = pi*r^2 = pi*d^2/4

A = pi*(1.80*10^-3)^2/4 = 2.54*10^-6 m^2

Since, mass = density*Volume = density*Area*length

mass/length = = density*Area

density of steel = 7800 kg/m^3 (Please Check this value in your reference book)

So,

= 7800*2.54*10^-6 = 19.8*10^-3 kg/m

So, Speed of wave will be:

V = sqrt (56.84/(19.8*10^-3)) = 53.578 m/sec

In two significant figures

V = 54 m/sec

Let me know if you've any query.