Teaching Physics with the Physics Suite Edward F. Redish

Displacement and velocity patterns in waves

The graphs below may represent either a picture of the shape of a wave on a string at a particular instant in time, t1, or the transverse (up and down) velocity of the mass points of that string at that time. Depending on what they are, the wave on the string may be:

1. a right going traveling wave
2. a left going traveling wave
3. a part of a standing wave growing in amplitude at time t1
4. a part of a standing wave shrinking in amplitude at time t1
For each of the following cases, decide what the wave is doing and choose one of the four letters (a)-(d).

1. Graph A is a graph of the string's shape and graph B is a graph of the string's velocity.
2. Graph A is a graph of both the string's shape and the string's velocity.
3. Graph B is a graph of the string's shape and graph A is a graph of the string's velocity.

Solution

i. a.
Since the parts of the string that are sloping downward are moving upward, and the parts of the string that are sloping upward are moving downward, the pattern will shift to the right.

ii. c.
Since the positive parts have positive velocities and the negative parts have negative velocity, the amplitude of the string is growing but the shape isn't changing.

ii. b.
Since the parts of the string that are sloping upward are moving upward, and the parts of the string that are sloping downward are moving downward, the pattern will shift to the left.