Question

A steel piano wire is 0.7 m long and has a mass of 5 g. It is stretched with a tension of 500 N. What is the speed of transverse waves on the wire? To reduce the wave speed by a factor of 2 without changing the tension, what mass of copper wire would have to be wrapped around the wire?

Answer 1

Answer:

a.264.6m/s

b.4995g

Explanation:

Data given,

Tension T=500N,

length of wire=0.7m,

mass,m=5g=0.005kg

a.To determine the speed of the transverse wave, we use the equation below

$V=\sqrt{\frac{FL}{m} } \\F=tension, L=length, m=mass$

if we insert values as given in the question , we arrive at

$V=\sqrt{\frac{500*0.7}{0.005}}\\ V=264.6m/s$

b. To reduce he wave speed by a factor of 2, the new wave speed will become 132.3m/s.

From the equation, if mass,m becomes subject of formula, we have

$m=\frac{V^{2}}{FL}\\ m=\frac{132.3^{2}}{500*0.7}\\m=50kg\\m=5000g$

Hence to reduce the speed by a factor of 2, (5000-5)g=4995g mass of copper wire would have to be wrapped around the wire.