Logitudinal and Transverse wave

[bchui]

Can anyone tell me the difference between logitudinal and transverse wave?
Could we actaully tell the difference from their given wave equation?

 

[quasar987]

In a transverse wave, the quatity that is oscillating is doing so in a direction perpendicular to the direction of propagation of the wave. Exemples: 1) Water waves: here, it is the water level that rises and sinks in the y direction but the disturbance is propagating in the x direction. 2) A (free) electromagnetic wave. Here is it the value of the E and B fields that each oscillate in plane perpendicular to the direction of propagation.

In a longitudinal wave, the thing that is oscillating is doing so in the direction of propagation. For exemple, the pressure in an air wave (sound).

There are waves that are neither too. The density wave in the air wave for instance. Density is not a vector, it just takes some value.

Wheter you can tell or not from just the wave equation is kind of an ambiguous question, because usually, what happens is that you start witj Newtonian mechanics, and you write the force equations and after a few manipulations, it becomes the wave equation. But by then, you know what is oscillating and you know in which direction. So you will probably write the wave equation for pressure as such:

$$v^2\partial_{xx} p_x(x,t)-\partial_{tt}p_x(x,t)=0$$

and by the x subscript it is apparent that is it the x-component of pressure that oscillates.

In an electromagnetic wave though, we start with a set of 4 equations, and we combine them to create a wave equation. Then we solve it, and THEN, we find that for it to satisfy the original 4 equations, the wave must be transverse. So in that case, we could not tell it is was transverse or longitidinal b4 solving it.

Wheter a wave is longitudinal or transverse is more or a physical thing than a mathematical thing you can see right from the wave equation.

 

[charng]

Yes, there are several key differences between longitudinal and transverse waves that can be observed from their wave equations.

Firstly, longitudinal waves are characterized by particle vibrations that are parallel to the direction of wave propagation, while transverse waves have particle vibrations that are perpendicular to the direction of wave propagation. This can be seen in the equations for each type of wave: for a longitudinal wave, the displacement of particles (y) is a function of the wave's propagation direction (x), while for a transverse wave, the displacement of particles (y) is a function of time (t).

Additionally, the speed of propagation for longitudinal waves is determined by the medium's density and elasticity, while the speed of transverse waves is determined by the medium's shear modulus and density. This means that longitudinal waves travel faster in denser, more elastic mediums, while transverse waves travel faster in mediums with higher shear modulus.

Another key difference is that longitudinal waves can travel through both solids and liquids, while transverse waves can only travel through solids. This is due to the fact that liquids do not have a shear modulus, which is necessary for transverse wave propagation.

In conclusion, while the wave equations for longitudinal and transverse waves may look similar, there are significant differences in the way they propagate and the mediums they can travel through. Therefore, it is possible to distinguish between these two types of waves based on their wave equations.