Chapter 11, Problem 51P

(a)

To determine

To Draw: The string shape when they directly overlap.

Explanation of Solution

Introduction:

When two or more waves overlap each other, the interference arises. The interference can be constructive or destructive depending upon how the troughs and crests of these waves meet.

The left wave pulse in the string is crest while the right one is trough. Therefore, the interference would be destructive.

Let, the amplitude of left pulse be $A_2$ and that of the right pulse be $A_1$ . Therefore, at the moment when two pulses overlap, the sketch of the string can be given as follow:

  

(b)

To determine

To Draw: The string shape after few moments.

Explanation of Solution

Introduction:

When two or more waves overlap each other, the interference arises. The interference can be constructive or destructive, depends upon how the troughs and crests of these waves meet.

A few moment later, the sketch of the string can be given as follow:

  

(c)

To determine

To Find: The energy when the string is straight.

Explanation of Solution

Introduction:

When two or more waves overlap each other, the interference arises. The interference can be constructive or destructive depends upon how the troughs and crests of these waves meet.

All particles of the string would be in equilibrium position due to the rest position of the string. Therefore, there would be no potential energy.

The particle of string would have only transverse velocity which corresponds to the transverse kinetic energy.

Conclusion:

Hence, the string would have transverse kinetics energy.