B Why longitudinal waves are waves?

They are wave-like. They behave according to the wave equation.

 

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.

 

Download WaveAdd, a free HTML5 wave addition simulation. I think that it will help you understand the differences and similarities between transverse waves and longitudinal waves.
Download it from:
'tinyurl.com/waveadd'

 

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.
You just can't win.

 

Is that a strict requirement?

 

I thought so. Am I mistaken?

 

http://physics.bu.edu/~duffy/HTML5/longitudinalwave.html



http://physics.bu.edu/~duffy/HTML5/wave.html


http://physics.bu.edu/~duffy/HTML5/longitudinal_wave.html

 

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 am also not sure I agree with Dale's answer that longitudinal waves "diffract, refract, and reflect," so what else could there be for them to be considered waves? A longitudinal wave in a slinky doesn't really have to diffract or even refract to be recognizable as a wave. The slinky wave does reflect, but then again so does a billiard ball rolling inside the slinky (assuming the ends are closed), and that clearly isn't a wave. It seems to me that there has to be more to being a wave than properties that follow from, e.g., the wave equation.

 

Can you give me an example?

 

Ocean waves are one familiar example.

 

How do those not obey the wave equation?

 

Aren't ocean waves a mix of longitudinal and transverse waves, which each of them obeying the wave equation?
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.

What is the definition of wave for you?

 

I'm not sure what kind of answer you're looking for here. For starters, water waves obey a different (Laplace's) 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.

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.

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):

 

@olivermsun what is the equation that governs ocean 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? You 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.

 

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.
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.