Question

FIGURE EX17.2 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s.

Short answer

Both waves will combine and the resultant wave will have double the amplitude of the initial waves due to superposition principle.

Step-by-step solution

Given info:

Two similar waves, both having positive amplitude are approaching each other with speed of 1m/s.

At t = 1sec

Both the waves have just come in contact and up till now no superposition will take place.

At t = 2sec

At t = 2 sec, waves have partially combined and due to superposition principle the mid region will rise up.

Height of mid region at t = 2sec will be $\frac{1}{2}cm+\frac{1}{2}cm=1cm$

At t = 3 sec

Both waves now perfectly overlap each other and due to super position principle their amplitude is doubled but width remains the same. Amplitude of resultant wave is 1cm + 1cm = 2cm.

At t = 4 sec

Snapshot at t = 4sec will be same as that of t = 2 sec, only this time waves are now moving apart from each other.

At t = 5 sec.

Snapshot at t = 5 sec will be same as that of t = 1 sec, only this time waves are now moving apart from each other.

At t = 6sec

At t = 6sec both waves are at the other wave's initial position, snapshot looks similar to t = 0sec but here waves are interchanged from that of t = 0 sec and are moving in opposite directions.