What distinguishes plane waves from wave packets in physics?

In summary, the difference between a plane wave and a wave packet is that a plane wave has infinite extent and is an idealization, while a wave packet has limited extent and is a more realistic description. Plane waves are said to be infinite in extent because of the adjective "plane," which means infinite in extent. A wave cannot have one frequency without being infinite in its "domain" because it must be modulated in order to localize it, which introduces other frequencies. The Fourier integral can account for both spatial and temporal truncation in a wave.
  • #1
gentsagree
96
1
Generally speaking, what is the difference between these two? What I mean by that is: in what kind of different processes are these produced (and used in physics)?
 
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  • #2
Plane wave has infinite extent and is an idealization that cannot actually occur in the theory. The wave packet is limited in extent and is more realistic description according to the theory.
 
  • #3
A 'packet wave' will consist of a range of frequencies, around the nominal frequency. A continuous wave (sinusoid) will, in the limit, consist of just one frequency.
 
  • #4
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?
 
  • #5
sigma_ said:
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?

It's a matter of definition. If the wave doesn't extend to infinity, it must be 'modulated' to localise it. If you modulate a continuous sinusoid, you introduce other frequencies (sidebands).
 
  • #6
sigma_ said:
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?

Because in "plane wave" you have the adjective "plane", which is by its meaning infinite in extent.

Frequencies have nothing to do with "plane wave". There are plane waves that have non-periodic profile, like ones used to model shock wave - when analyzed into Fourier integral, all possible frequencies are present.
 
  • #7
sophiecentaur said:
It's a matter of definition. If the wave doesn't extend to infinity, it must be 'modulated' to localise it. If you modulate a continuous sinusoid, you introduce other frequencies (sidebands).
Got it. Thanks
 
  • #8
sigma_ said:
Got it. Thanks

Btw, that Fourier business works for spatial truncation too. That accounts for diffraction at a boundary.
 

1. What is the difference between a plane wave and a wave packet?

A plane wave is a type of wave in which the wavefronts are parallel to each other, meaning that the wave travels in a straight line. On the other hand, a wave packet is a combination of multiple plane waves with different wavelengths and directions, resulting in a localized wave with a varying amplitude and frequency.

2. How do plane waves and wave packets behave differently?

Plane waves propagate at a constant velocity and do not change their shape or amplitude as they travel. In contrast, wave packets disperse and spread out as they propagate, and their shape and amplitude change over time.

3. What are some real-world examples of plane waves and wave packets?

Plane waves can be seen in electromagnetic radiation, such as radio waves and light, as well as in sound waves. Wave packets can be observed in phenomena such as ocean waves, earthquakes, and quantum particles.

4. Which type of wave is more commonly encountered in everyday life?

Plane waves are more commonly encountered in everyday life, as they are the basis for many types of waves that we interact with, such as light and sound. However, wave packets are also present in certain everyday phenomena, such as ocean waves and sound echoes.

5. Can a plane wave be transformed into a wave packet, and vice versa?

Yes, a plane wave can be transformed into a wave packet through a process called wave packet modulation, where multiple plane waves with different frequencies and directions are combined to create a localized and varying wave. Similarly, a wave packet can be transformed into a plane wave through a process called wave packet demodulation, where the different frequencies and directions are separated and the wave packet is "unpacked" into individual plane waves.

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