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i know it's an absurd question, but why are longitudinal waves called waves although they aren't wave-like?
They are wave-like. They behave according to the wave equation.i know it's an absurd question, but why are longitudinal waves called waves although they aren't wave-like?
They diffract, refract, and reflect. I am not sure what is left to be considered wave-likei know it's an absurd question, but why are longitudinal waves called waves although they aren't wave-like?
If you plot pressure (or whatever) versus position and look at the resulting graph as it evolves over time, the "90 degrees" is not physical. It is the fact that there are two [mostly] orthogonal variables that are plotted at 90 degrees from one another on the graph paper.Perhaps you mean they don't look instantly recognizable as sine waves? There's a sine wave in there, it's just rotated 90 degrees, flattening it.
I think we mostly agree, but will separate:If you plot pressure (or whatever) versus position and look at the resulting graph as it evolves over time, the "90 degrees" is not physical. It is the fact that there are two [mostly] orthogonal variables that are plotted at 90 degrees from one another on the graph paper.
Not too absurd, actually - if you are comparing them with waves on water, where the motion of the water appears to be 'up and down'. However, as the water moves 'obviously' up and down, it is also moving forward and backwards (taking water from the troughs and putting it in the peaks). i.e. there is also a significant Longitudinal component. Most cases are a mixture of transverse and longitudinal waves, once the amplitude gets large. Even Electromagnetic Waves passing through a medium can have slight longitudinal component, despite what we say about radio waves being Transverse.i know it's an absurd question, but why are longitudinal waves called waves although they aren't wave-like?
Is that a strict requirement?They are wave-like. They behave according to the wave equation.
I thought so. Am I mistaken?Is that a strict requirement?
There are many examples of waves that do not behave much like the wave equation, so I don't think the wave equation can be the defining feature for what makes a wave.I thought so. Am I mistaken?
Can you give me an example?There are many examples of waves that do not behave much like the wave equation, so I don't think the wave equation can be the defining feature for what makes a wave.
How do those not obey the wave equation?Ocean waves are one familiar example.
Aren't ocean waves a mix of longitudinal and transverse waves, which each of them obeying the wave equation?Ocean waves are one familiar example.
I'm not sure what kind of answer you're looking for here. For starters, water waves obey a different (Laplace's) equation.How do those not obey the wave equation?
No. The motion of ocean waves is orbital. The water moves in both the longitudinal and transverse directions, but it isn't a mix of two distinct waves. In fact, the two types of motion can't be independent if you want to satisfy conservation of mass.Aren't ocean waves a mix of longitudinal and transverse waves, which each of them obeying the wave equation?
It might be more useful to say that we have dispersion in ocean waves because they are governed by a different physics than the wave in a string.Is it because we have dispersion in ocean waves? Even with dispersion, each unique frequency component obeys a unique wave equation, but yes the wave as a whole doesn't obey the standard wave equation.
It's pretty hard to come up with a definition of a wave that encompasses all the things we think of as waves. "You'll know it when you see it" might be about as good as it gets. To quote Whitham (1974):What is the definition of wave for you?
Various restrictive definitions can be given, but to cover the whole range of wave phenomena it seems preferable to be guided by the intuitive view that the wave is any recognizable signal that is transferred from one part of the medium to another with a recognizable velocity of propagation...This may seem a little vague, but it turns out to be perfectly adequate and any attempt to be more precise appears to be too restrictive; different features are important in different types of waves.
The equation resulting from solving an equation of the 'motion' of the particles (or variation of the fields) for all waves has so much in common that I would say it is a better description than anything else about a general Wave.Is that a strict requirement?
As I said above, it’s Laplace’s equation (elliptic), not the wave equation (hyperbolic). This is true not just for water waves but for a whole class of important flows.@olivermsun what is the equation that governs ocean waves?
The physical interpretation for why the longitudinal and transverse components of a water wave have to be related is that the water volume has to be conserved. For example, if the surface moves upward, then water has to move in from the sides and/or below to fill that volume. This remains true for linear(ized) waves.I suspect the equation or set of equations isn't linear and that's one of the reason we cant speak about separate longitudinal and transverse components?
1) see aboveYou say that they satisfy Laplace's equation, but Laplace's equation is
1) linear
2) doesn't contain the time variable, so the full equation must be something else.
But it is generally untrue that wave solutions look alike, except that they propagate while remaining “recognizable” in some way.The equation resulting from solving an equation of the 'motion' of the particles (or variation of the fields) for all waves has so much in common that I would say it is a better description than anything else about a general Wave.
I agree that the “sine wave criterion” is a red herring, but you also seem to mixing up several different phenomena.The sine wave thing is really a bit of a red herring here because the shape of a wave depends more on the variations of the generator that causes the waves. There are many waves of very short duration (single pulses are very common) that are definitely not sinusoidal yet they are still waves.
This is a B level thread. It's easy to leave an OP behind if a thread gets too advanced.But it is generally untrue that wave solutions look alike, except that they propagate while remaining “recognizable” in some way.
I agree that the “sine wave criterion” is a red herring, but you also seem to mixing up several different phenomena.
A hyperbolic wave, like the linear wave in the string, can travel very long distances while retaining almost any initial shape, including isolated pulses.
On the other hand, the shape of dispersive waves can evolve to be nearly independent of the details of their generation. Think of nearly monochromatic (sinusoids) “sets” of ocean waves arriving at a surfers’ beach.
If nonlinearity is added to the system, then you can have yet another possibility: special solutions (e.g., solitons) can arise in which nonlinearity and dispersion balance each other out. In this case certain waves propagate without changing shape, while most other waves still look dispersive.