Question

One metre long wire is fixed between two rigid supports. The tension is the wire is $200N$ and mass per unit length of the wire is $\mu =2x$, where $x$ is the distance from one end of the wire. Find the time (in second) the pulse takes to reach the other end of the wire

Answer 1

Answer: 0.067

The pulse velocity is given by,
$v=\sqrt{\frac{F}{\mu }}=\sqrt{\frac{200}{2x}}=\frac{10}{\sqrt{x}}$
or $\frac{dx}{dt}=\frac{10}{\sqrt{x}}$
or $\underset{0}{\overset{1}{\int }}\sqrt{x}dx=10\underset{0}{\overset{t}{\int }}dt$
or $\underset{0}{\overset{1}{\int }}{x}^{12}dx=10\underset{0}{\overset{t}{\int }}dt$
or ${\left|\frac{x^{3/2}}{3/2}\right|}_0^1=10t$
or $t=\frac{2}{30}s=0.067s$