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Wave equation

  1. Oct 29, 2009 #1
    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. jcsd
  3. Oct 29, 2009 #2

    Born2bwire

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    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.
     
  4. Oct 29, 2009 #3
    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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  5. Oct 30, 2009 #4

    Born2bwire

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    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.
     
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