lo3 position and time plots
TRANSCRIPT
Jessica Weng
Phys 101
Section 203
Position PlotsAlso 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
QuestionDetermine the wavelength and the wave number of the
following graph.
HintWavelength 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
Solution
Wavelength = π
Wave number = 2 π / wavelength
= 2 π / π
= 2
Time PlotAlso 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
Question
Rank the period of the following graphs from highest to lowest.
a)
b)
c)
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
Solution
c> a=b
Period of c = π
Period of a and b = π/2
A Comprehensive QuestionSuppose 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.
SolutionAmplitude 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
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 φsin φ = 0
φ = 0
Solution (Cont’d)Wave equation for graph c:
D (x,t) = 1.5 sin (2x – 2t)
Thanks for watching!