lo3 position and time plots

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!