A cord of mass 0.65 kg is stretched between two supports 8.0 m apart. If the tension in the cord is 120 N, how long will it take a pulse to travel from one support to the other?

Whenever a wire string of specific length fix between two supports and a small disturbance create, then there would be propagation of a wave. The velocity of the wave can obtain with the help of tension of string, mass, and length of the string.

The given data can be listed below as,

• The mass of a cord is,\(m = 0.65\;{\rm{kg}}\).
• The distance between two supports is,\(l = 8.0\;{\rm{m}}\).
• The tension in the cord is,\(T = 120\;{\rm{N}}\).

The speed of the transverse wave in the string can be expressed as,

\(\begin{aligned}{c}v &= \sqrt {\frac{T}{\mu }} \\ &= \sqrt {\frac{T}{{\left( {\frac{m}{l}} \right)}}} \\ &= \sqrt {\frac{{Tl}}{m}} \end{aligned}\)

Here, \(v\) is the speed of the transverse wave in the string, \(\mu \) is the mass per unit length and \(l\) is the length of the string.

The expression of the time taken by the pulse to travel from one support to other is given by,

\(\begin{aligned}{c}t &= \frac{l}{v}\\ &= \frac{l}{{\sqrt {\frac{{Tl}}{m}} }}\end{aligned}\)

Here,\(t\)is the time taken by the pulse to travel from one support to other.

Substitute all the known values in the above equation.

\(\begin{aligned}{c}v &= \frac{{\left( {8.0\;{\rm{m}}} \right)}}{{\sqrt {\frac{{\left( {120\;{\rm{N}}} \right)\left( {8.0\;{\rm{m}}} \right)}}{{0.65\;{\rm{kg}}}}} }}\\ &\approx 0.21\;{\rm{s}}\end{aligned}\)

Therefore, the time take by the pulse to move from one support to other is \(0.21\;{\rm{s}}\).