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Physics Lesson 19.5.2 - Definition and Features of Wave Packet

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Welcome to our Physics lesson on Definition and Features of Wave Packet, this is the second 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.

Definition and Features of Wave Packet

A "wave packet" is a fragmented or a discrete wave. It represents a short or a burst wave All sources that operate periodically in short intervals emit wave packets. Therefore, a wave packet has a limited width in space. The spatial extension Δx of a wave packet is given by the equation

∆x ≈ v ∙ ∆τ

where v is the packet's speed and Δτ is the time interval between two consecutive emissions.

Example 1

Calculate the spatial extension of a radio-wave packet emitted by an AC source in any country in Europe.

Solution 1

Clues:

(v = c = 300 000 km/s = 3 × 108 m/s)
Δx = ?

We know that the frequency of all AC sources in Europe is f = 50 Hz. Therefore, the source oscillates in time intervals of

T = 1/f = 1/50 Hz = 0.02 s

This value corresponds to the time interval between two consecutive emissions from the source. Thus, we have

∆τ = T = 0.02 s
= 2 × 10-2 s

Hence, since the spatial extension of a wave packet is given by

∆x ≈ v ∙ ∆τ

we obtain after substitutions:

∆x ≈ v ∙ ∆τ
= c ∙ ∆τ
= (3 × 108 m/s) ∙ (2 × 10-2 s)
= 6 × 106 m
= 6000 km

Since the extension of this packet is very large, we can consider this wave as an ideal standing wave.

Now, let's consider another example but this time, the wave source is an atom.

Example 2

Calculate the spatial extension achieved by a photon emitted by an atom during the time interval of 10-9 s.

Solution 2

Clues:

Δτ = 10-9 s
(c = 3 × 108 m/s)
Δx = ?

Giving that

∆x ≈ v ∙ ∆τ

we obtain after substitutions:

∆x ≈ v ∙ ∆τ
= c ∙ ∆τ
= (3 × 108 m/s ∙ (10-9 s)
= 0.3 m

From the result, you can see that the EM wave packets emitted by atoms are very concentrated. This allows us visualize the photon as a particle.

Advanced theoretical calculations show that any wave packet does not contain a single a single wavelength but an infinite number of wavelengths instead. These values range from λ - λ/2 to λ + λ/2, where λ represents the mean wavelength of wave packet. The width Δλ of such wave packets relates to its spatial extension through the relation:

∆x ∙ ∆λ ≈ λ2/2π

This relation is characteristic for any wave group or packet, whose shape is shown in the figure below.

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

Example 3

Calculate the wave width of a photon and compare it to the mean wavelength (λ = 600 nm) given that its spatial extension is Δx ≈ 0.3 m.

Solution 3

Clues:

Δλ = ?
Δx = 0.3 m
λ = 600 nm = 6 × 10-7 m

Applying the equation

∆x ∙ ∆λ ≈ λ2/2π

we find for the wave width Δλ after substituting the known values:

∆λ ≈ λ2/2π ∙ ∆x
= (6 × 10-7 m)2/2 ∙ 3.14 ∙ (0.3 m)
= 1.91 × 10-13 m

This result means the wave width of photon is much shorter (about 300 000 times shorter) than its average wavelength. This results in an almost continuous type of photons emission, which makes the identification of the discrete nature of light very difficult.

You have reached the end of Physics lesson 19.5.2 Definition and Features of Wave Packet. 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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