1. Jessica Weng
Phys 101
Section 203

2. Position Plots
 Also called snapshot graphs
 Fixed time t
 plot displacement as a function of
position
Shows the displacement of every
section of the medium
 Determine from it:
 Amplitude: maximum displacement
 Wavelength: shortest distance over which
a wave repeats

3. Question
Determine the wavelength and the wave number of the
following graph.

4. Hint
 Wavelength can be read off position plot as
it is the distance between 2 adjacent
repeating points
 May be easier to use crests or troughs
 Wave number = 2π / λ = 2π / wavelength

5. Solution
 Wavelength = π
 Wave number = 2 π / wavelength
= 2 π / π
= 2

6. Time Plot
 Also called history graph
 Fixed position
 plot displacement as a function of time
Shows how the displacement of a given
point varies with t
Determine from it:
 Amplitude: maximum displacement
 Frequency: how many cycles pass
through this given point in 1 second

7. Question
 Rank the period of the following graphs
from highest to lowest.

8. a)

9. b)

10. c)

11. Hint
• General equation of sinusoidal wave:
2πf = 2π/T
T = 1/f
•Period can be read off a time plot as it is
the shortest time before a wave repeats

12. Solution
 c> a=b
 Period of c = π
 Period of a and b = π/2

13. A Comprehensive Question
 Suppose graph c is obtained at x = 0 m and
the wave in graph c has a wave speed of 1.0
m/s. Determine the amplitude, frequency,
angular frequency, wavelength, phase
constant of the wave and write a
displacement equation for the wave.

14. Solution
 Amplitude can be read off time plot as it is
the maximum displacement: 1.5
 Frequency = 1 / T = 1 / π
 Angular frequency = 2π / T = 2π / π = 2
 Wavelength:
 Wave speed = wavelength x frequency
 Wavelength = v / f = 1 / (1 / π) = π

15. Solution (Cont’d)
Above is the general equation for sinusoidal waves
Plug in known values to find phase constant:
D (x,t) = 1.5 sin (2x – 2t + φ)
D(0,0) = 1.5 sin (φ)
0 = 1.5 sin φ
sin φ = 0
φ = 0

16. Solution (Cont’d)
 Wave equation for graph c:
D (x,t) = 1.5 sin (2x – 2t)

17. Thanks for watching!