Question

A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to the other?

Answer 1

Concepts and reason

The concepts required to solve the given problem are tension, velocity, and linear mass density.

Initially, calculate the linear mass density of the cord by using the relation between mass and linear mass density. Next, calculate the speed of the wave by using the relation between velocity, tension, and linear mass density. Finally, calculate the time taken to travel the pulse from one support to another support by using relation between velocity and distance.

Fundamentals

The mass per unit length of the string is called as linear mass density.

The expression for the linear mass density is,

$\mu = \frac{m}{L}$

Here, m is the mass and L is the length of the string.

The expression for the speed of a wave on the string is,

$v = \sqrt {\frac{T}{\mu }}$

Here, T is the tension and $\mu$ is the linear mass density.

The rate of change in distance is called as velocity.

$v = \frac{d}{t}$

Here, d is the distance and t is the time.

The speed of the pulse is,

$v = \sqrt {\frac{T}{\mu }}$

Substitute 0.023kg/m for $\mu$ and 150 N for T in the above equation.

$\begin{array}{c}\\v = \sqrt {\frac{{150\;{\rm{N}}}}{{0.023\;{\rm{kg/m}}}}} \\\\ = 80.75\;{\rm{m/s}}\\\end{array}$

The time taken to reach the opposite end of the string is,

$t = \frac{L}{v}$

Substitute 28 m for L and 80.75 m/s for v in the above equation.

$\begin{array}{c}\\t = \frac{{28\;{\rm{m}}}}{{80.75\;{\rm{m/s}}}}\\\\ = 0.346\;{\rm{s}}\\\end{array}$

Ans:

The time required to travel the pulse from one support to another support is 0.346 s.