# Wave equation

1. Oct 29, 2009

### Rustydorm

Hi

I have a case where a wave with an amplitute 'A' progresses with a particular velocity 'v'. The wave is such that the amplitude at x=0 increases to particular value and stays there for the entire time

some thing like below.

at time(t)=0
x(position) = 0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1
y(Amplitude) =1,0,0,0,0,0,0,0,0,0

at t=1
x= 0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1
y=1,1,0,0,0,0,0,0,0,0

at t=2
x= 0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1
y=1,1,1,0,0,0,0,0,0,0

at t=3
x= 0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1
y=1,1,1,1,0,0,0,0,0,0

and so on....until for all of x values, y = 1

This is for discrete points. Is there any continuous function for this kind of wave?

Can you define this wave using a equation or a mathematical function? How do you call this wave? Anyone kindly help me with it. I am expecting a function with variables such as y= f(A,v,x,t).

Thanks :)

2. Oct 29, 2009

### Born2bwire

Unless the ramp-up for the wave is much faster than the wave velocity (which means your spatial sampling is insufficient), then this is going to be a discontinuous wave. Just looks like a propagating step function to me.

3. Oct 29, 2009

### Rustydorm

Thanks Born2bwire. If the ramp up is almost instantaneous, then just the front of the wave will be moving at a particular velocity. At a particular x, at one discrete time y=0 and the next discrete time y=1

If it helps, I have attached a graph of the progressing wave.

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4. Oct 30, 2009

### Born2bwire

Under those conditions then you will have a discontinuous function, the step function. For your case we can simply define it as

f(x) = 1 if x<= 0; 0 else

So then the wave equation would be y=A*f(x-v*t), where the velocity v here is .1 units of distance per units of time.

If you require a continuous function though, we would have to reformulate f(x-v*t) to be a function with a continuous, but fast ramp up.