This document discusses position and time plots used to analyze waves. Position plots show displacement as a function of position for a fixed time, like a snapshot. Time plots show displacement as a function of time for a fixed position, like a history. Both are used to determine characteristics like amplitude, wavelength, frequency, and phase from a wave graph. The document provides examples of questions identifying these characteristics from sample position and time plots and works through the solutions.

1. Chapter 14 Waves:
Position Plots and Time Plots

2. 3-D Graphs
• A plot of D (x,t) as a function of position x and
time t results in a 3-D graph.
– Position along the x-axis
– Time along the y-axis
– Displacement D(x,t)
– along the z-axis

3. • While visually helpful, it makes it difficult to
determine the wavelength, frequency,
amplitude and phase constant
• Thus we use plots where one variable is kept
constant, and the wave f(x) is plotted against
the other variable

4. Position Plots
• Time is fixed; wave function is plotted as a
function of position (x)
• Shows Δd of every section of the medium at a
fixed time
• Like taking a snapshot: “Snapshot Graphs”

5. Position Plots (cont’d)
What is the amplitude of this graph?
a) 3
b) 6
c) 1.5
d) 1

6. Position Plots (cont’d)
What is the amplitude of this graph?
a) 3
b) 6
c) 1.5
d) 1
The maximum displacement of a point
Is +/- 1.0 m, therefore A= 1.0 m

7. Position Plots (cont’d)
What is the wavelength of this graph?
a) 3
b) 6
c) 1.5
d) 1

8. Position Plots (cont’d)
What is the wavelength of this graph?
a) 3
b) 6
c) 1.5
d) 1
The distance from one crest to crest, or one
Trough to trough is 3 m.
For example, x=3 at point A and x=6 at point B.
Therefore wavelength = 6.0 m – 3.0 m = 3.0 m
Pt.A Pt. B

9. Time Plots
• The wave function D(x,t) is plotted as a
function of time for a fixed position.
• The time plot shows how the displacement of
a given point of the medium varies with time
• “History Graphs”

10. Time Plots
• What is the Amplitude of this graph?
• A) 0.5 m
• B) 0.4 m
• C) 4.0 m
• D) 2.0 m

11. Time Plots
• What is the Amplitude of this graph?
• A) 0.5 m
• B) 0.4 m
• C) 4.0 m
• D) 2.0 m
The maximum displacement of a point
Is +/- 0.5 m. Therefore A= 0.5 m

12. Time Plots
• What is the wavelength of this graph?
• A) 0.5 m
• B) 40 m
• C) 90 m
• D) 128 m

13. Time Plots
• What is the wavelength of this graph?
• A) 0.5 m
• B) 40 m
• C) 90 m
• D) 128 m
This ones a bit trickier.
a) Solve for the period T
a) Pt B- Pt A = 6.4 s
Wavelength = v/f = vT
(20 m/s) (6.4) = 128.0 m

14. Position and Time Plots
• For more help/information, refer to pages
211-213 of Physics: for Scientists and
Engineers, An Interactive Approach (text)