Let me imagine that air nearby has structure like this, meaning that pressure variation without any disturbance is almost equal.
Now if I speak, I set some molecules of it in motion. They move with a velocity $v$ and sets motion to the molecules next to them. With every collision, either their amplitude must decrease or they are not losing energy. But in a graphical representation of the same, they are shown as
In each of the representation above, the crests and the troughs at any point lie on the same line. That is the amplitude, even after much time is equal. Does this mean that amplitude will always be equal no matter how much time passes? That doesn't seem real as the molecules set next molecules in motion with 'some of its energy' and not complete energy. If they provided complete energy they wouldn't have get back to their mean position.
Also the difference between two crests and two rarefactions (that is the wavelength) is equal. How is this possible? at the very start the particles move at a different speed, then they lose some energy to move the next particle. So when the next particle will move the third one, the speed will not be exactly same to the first one and after collision second one will also lose some energy taking even more time to get back to it's mean position. Let me explain it like an equation.
Let's say particle 1 has a speed of V when it is vibrated. Then it moves and vibrates another particle, losing some of it's energy hence resulting in lesser speed. Now it has a speed U.
Particle 2 got some of the energy of particle 1 and got a speed of $v$. It moves and vibrates Particle 3, again losing some of it's energy hence less speed. now its speed is $u$.
So, V > v & U > u
Also V > U & v > u
During oscillation 1st, wave will move with speed V, U
During oscillation 2nd, wave will move with speed v, u
The crest thus formed will be in distance => Ut + vt
and trough thus formed will be in distance => vt + ut
at the same time, distance of crest will be less, as Ut > ut (vt is common) and the distance of trough will be more. Then how come wavelength can be equal, which is defined as the distance of two crests or two rarefactions?
Another question is how the graph is formed of a sound wave. If we make graph, taking some point as a mean position then there will be only one crest and one trough and the rest will be a straight line. If we are change our point every second then which point are we taking, see the graph of a longitudinal wave,
As I can see, there is always a point where air is compressed and there is always a point where air is forming rarefaction. If I follow wave, I can always show the air to be compressed or having rarefactions and if I don't follow then there will be a graph with only 1 crest and 1 compression.
Summarizing the questions, they are as follows:
Does this mean that amplitude will always be equal no matter how much time passes? if not, why they are shown like that in graph?
How is the difference between between two crests and two troughs are equal?
How is a sound wave represented with graphical method?
Any edits or clarification about some topic which I'm confused on will be welcomed.