Chapter 15, Problem 1P

To determine

Whether, the pulse travels faster, slower or at a constant speed when it travels toward the ceiling.

Answer to Problem 1P

Pulse travels faster toward the ceiling.

Explanation of Solution

Introduction:

Speed of the pulse depends on the medium properties.

A pulse travelling on a rope or string depends on the tension in the rope/string and the linear mass density of the rope/string.

The relation between the speed and other two quantities is given as:

  $v=\sqrt{\frac{T}{m}}$

Where, T is the tension in the rope and m is the linear lass density which is the ratio of the mass of the rope and the length of the rope.

If one considers a small part of the rope near the ceiling, it is under the maximum tension as it is being pulled by rest of the length of the rope. The portion of the rope at the open end is under the least tension. Hence, the tension in the rope increases from open end to hanging end.

As speed is directly proportional to the tension, therefore, speed of the pulse will increase while travelling in upward direction.

Conclusion:

Thus, when the tension in the rope will increase, the pulse speed increases as it moves towards the ceiling.