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Physics Lesson 19.5.1 - Recalling the Simple Harmonic Wave (Oscillation)

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Welcome to our Physics lesson on Recalling the Simple Harmonic Wave (Oscillation), this is the first lesson of our suite of physics lessons covering the topic of Electromagnetic Wave Packet. The Uncertainty Principle, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Recalling the Simple Harmonic Wave (Oscillation)

We know that the position (in two dimensions) of any point of a standing wave is expressed through the sinusoidal equation of simple harmonic motion, that is

y(t) = ymax ∙ sin(ω ∙ t - k ∙ x)

where

y(t) is the y-coordinate of a given point of a wave at any instant t,

x is the x-coordinate of the given point of wave (it is up to us to choose any point we want, so the x-coordinate depends on our choice),

t is the time instant in which we are interested to know the position of the given point of wave,

ω = 2π · f is the angular frequency of wave, and

k = 2π/λ is the wave number - a feature that depends only on the wavelength.

Thus, the above equation can also be written as

y(t) = ymax ∙ sin(2π · f ∙ t - 2π/λ ∙ x)

The shape of the simple harmonic wave in two dimensions is shown below.

Physics Tutorials: This image provides visual information for the physics tutorial Electromagnetic Wave Packet. The Uncertainty Principle

For simple harmonic waves, frequency is determined by the features of emitting source, hence it can be considered as constant. The same for wavelength if the wave is propagating in a homogenous medium (where the wave speed is the same throughout the entire medium), given the equation of waves

v = λ ∙ f

Such waves (with constant frequency) are emitted from sources that oscillate unceasingly in a periodic fashion. In these conditions, the wave would propagate in space up to infinity (ideal or standing waves). Obviously, in the real world this cannot occur, as the environment will eventually drain up the wave's energy. However, if we consider short intervals of time up to few minutes, many real waves behave in a similar way as ideal waves. For example, a sound source, a radio emitter etc., can be described using the standing wave pattern.

The approach is different when considering the oscillation of atoms, molecules or other microscopic particles however. Despite they represent EM sources too, their radiation is discrete (with interruptions). A single radiating action produced by atoms is very short; it lasts a few nanoseconds (1 ns = 10-9 s). Therefore, when studying the radiation of atoms, we always refer to "wave packets" instead of individual waves. Likewise, photons are also emitted in wave packets.

You have reached the end of Physics lesson 19.5.1 Recalling the Simple Harmonic Wave (Oscillation). There are 5 lessons in this physics tutorial covering Electromagnetic Wave Packet. The Uncertainty Principle, you can access all the lessons from this tutorial below.

More Electromagnetic Wave Packet. The Uncertainty Principle Lessons and Learning Resources

Modern Physics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
19.5Electromagnetic Wave Packet. The Uncertainty Principle
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
19.5.1Recalling the Simple Harmonic Wave (Oscillation)
19.5.2Definition and Features of Wave Packet
19.5.3The Uncertainty Relation for EM Wave Packet (Photon)
19.5.4De Broglie's Wave Packet. Wave Width and Uncertainty of Momentum
19.5.5Heisenberg's Uncertainty Principle

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