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Wize University Physics Textbook (Master) > Waves: Mechanical

Snapshots and History Plots

Traveling WavesPrevious Section
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Snapshots and History Plots

Since traveling waves are functions of two variables, position xx and time tt, we can better analyze their behavior if we "freeze" one of the variables, and see what happens when the other one varies.

  • The pattern for the oscillation of a single particle of the rope in time is known as the history plot (wave displacement at a specific x\colorThree{\bf{x}})








  • The spatial shape of the wave at any instant has a repetitive pattern. This is known as the snapshot of the wave (wave displacement at a specific y\colorFour{\bf{y}})








Example: History Plot

Looking at the behavior of the string at x=0x=0, we graph the following behavior (yy is measured in cm, tt is measured in seconds):


What is the wave's speed of propagation?

A) 11 cm/s
B) 0.250.25 cm/s
C) π/2\pi/2 cm/s
D) 00 cm/s
E) Not enough information

To find the speed of propagation of wave, we need a pair of quantities: (ω,k)(\omega,k) or (T,λ)(T,\lambda).

From this one graph, we can find the period: T=4 sT=4\ \mathrm{s}

and angular frequency: ω=2π/T=π/2 (rad/s)\omega=2\pi/T=\pi/2\ (\mathrm{rad}/\mathrm{s})

But we cannot find the wave number kk nor the wavelength λ.\lambda.

Therefore, we do not have enough information to find the speed of propagation: answer is E).

Watch Out!
One might be tempted to construct the velocity vy=−ωAsin⁡(ωt+ϕ)v_y = -\omega A \sin(\omega t+\phi) from this graph, but this is the particle velocity, and NOT the speed of propagation.


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Practice: Snapshot and History Plots


The history and snapshot plots of a wave traveling in the direction of positive xx follow.
Write the displacement equation of the wave. Draw the snapshot plot T/2T/2 s after t=1t=1.