What do the graphical representations of waves actually represent?

[harjyot]

I know how waves work, by the oscillation of particles along there mean position..fine
I know how a simple oscillatory motion can be described by a sinusoidal wave , and what is its physical significance...okay
but what I don't understand when waves (say a transverse) wave is represented by a sinusoidal wave , what is it representing? how is it 'travelling/

 

[HallsofIvy]

If you are talking about waves on, say, a rope, even in that "one dimensional" situation involves two variables, x and t. The sine curve is the rope "frozen" at a given time t. Its height represents heighrt of that particular point on the rope at that particular time.

 

[harjyot]

I am talking about what a waveform graph actually shows

 

[Pythagorean]

It only shows the relationship between independent and dependent variables, like any other plot.

Plots allow us to translate mysterious quantities (like pressure or electromagnetic intensity) into our comfortable domain of understanding: space. All plots are simply a property to space translation, we translate things like pressure as a function of time (P and t) into a comparison of two spatial directions (x and y)

 

[jbriggs444]

A typical graph will capture only a partial description of the wave.

Looking at a cross section of a water wave, for instance could tell you the height of the water surface at each point. But it would not tell you about the corresponding motion of the water.

A snapshot of a water wave that looks like a pure sine wave is consistent with a wave traveling right to left. It is also consistent with a wave traveling left to right. It is consistent with a wave form that oscillates in place. And it is consistent with infinitely many other superpositions of these.

Other waves are analagous. The y coordinate on the graph of a compression wave might indicate pressure. The y coordinate on the graph of a transverse wave might indicate displacement. The y coordinate on the graph of an electromagnetic wave might indicate electric field strength. In each case the graph fails to capture a complete enough description to predict which way the wave is travelling.

 

[Bobbywhy]

The links on this page contain mathematically correct animations which visualize a number of topics involving waves and oscillation.

http://www.acs.psu.edu/drussell/demos.html

 

[sophiecentaur]

I know how waves work, by the oscillation of particles along there mean position..fine
I know how a simple oscillatory motion can be described by a sinusoidal wave , and what is its physical significance...okay
but what I don't understand when waves (say a transverse) wave is represented by a sinusoidal wave , what is it representing? how is it 'travelling/

That's fair enough but a wave is not just an oscillation in time, a wave involves distance and time.
If you can bear to look at the simplest mathematical way of describing things:
An oscillation can be written
A = A₀ sin(ωt)
but the equation of a wave looks like
A = A₀ sin(ωt -kx)

If you choose a fixed position (x value) the Amplitude A follows a sinusoidal variation with time (any one section of a vibrating string just goes up and down) and if you choose a fixed time (a snapshot) the variation over distance (x) is also a sinusoid. Lumping the two together, you get a sinewave that moves from left to right. There is a delay (Phase) in the vibrations, the further you go to the right.
It is the fact that one part of the string (or whatever else is carrying the wave) will only start to move after the previous part has already moved (pulled it) and the next part will move after a similar delay so the 'disturbance' is passed along. If the string is very taught, the delays will be less and the wave will travel faster. If the string is very slack (or very heavy) the delays will be greater and the speed will be slower.