Chapter 11, Problem 41P

To determine

To Calculate: The time taken by the pulse.

Answer to Problem 41P

The time taken by the pulse to travel from one support to other support is $0.35\text{ s}$ .

Explanation of Solution

Given info:

Mass, $m=0.65\text{ kg}$

Stretching between two supports, $\Delta x=28\text{ m}=L$

Tension in the cord, $T=150\text{ N}$

Formula used:

To find the time taken by the pulse to travel from one support to other support, velocity of the pulse from the cord must be known. To find the velocity of the cord following formula is used,

  $v=\sqrt{\frac{T}{\left(\frac{m}{L}\right)}}=\frac{\Delta x}{\Delta t}$

Here,

  $v$ is velocity of cord,

  $T$ is tension in the cord,

  $m$ is the mass of cord,

  $\Delta x$ is the stretching between two supports.

Calculation:

Substitute the given values in the above equation,

  $\begin{array}{l}v=\sqrt{\frac{150}{\left(\frac{0.65}{28}\right)}}=\frac{28}{\Delta t}\\ \Delta t=\frac{28}{\sqrt{\frac{150}{\left(\frac{0.65}{28}\right)}}}=0.35\text{ s}\end{array}$

Conclusion:

Thus, the time taken by the pulse to travel from one support to other support is $0.35\text{ s}$ .