In my school textbook, the chapter about Trig demonstrates a function to replicate waves in water when a stone is thrown in. The function is:

$$f(t,r)= {\alpha\sin(\beta r+\gamma t)\over\{t(r+1)\}^\delta}$$

It shows a picture of what the wave looks like with some unstated values for $\alpha,\beta, \gamma,$ and $\delta$, and it results in a nice smooth wave. When I try to input this function into Wolfram|Alpha, I don't get a smooth wave, I get a really jacked-up wave (if it even is a wave).

Can anyone instruct me as to how I need to input this to get the simulation to work properly?

Extra Info: $t =$ time elapsed and $r =$ distance traveled from the center point of impact

:The function is only defined for all $t\neq0$ and $r\neq-1$

:$\alpha$ controls the wave height, $\beta$ controls wave spacing, $\gamma$ controls the travel rate of the waves, and $\delta$ controls the decrease in wave height with time and distance.


1 Answer 1


Everything stands and falls with $\delta$.

With $\delta<0.5$ every value of $\alpha,\beta,\gamma$ seems to work fine.

Here you have $\alpha=1,\beta=1,\gamma=1,\delta=0.1$ enter image description here

As a revolutionplot with fixed $t$

enter image description here

With a dynamic updating t: $0.2\leq t\leq 10$. Interestingly, the time direction seems to have the wrong sign.

enter image description here

And explicit for OP a string for $t=1$ for Wolfram|Alpha

plot3d Sin[Sqrt[x^2+y^2]+1]/((Sqrt[x^2+y^2]+1)^0.1) for x from -10 to 10, y from -10 to 1

  • $\begingroup$ There must be something wrong with how the function is given in the text book. The book shows the wave looking like this. What I get, though, is something really jagged and wonky with a height of between 0.005 and 0.01 depending on the variables. $\endgroup$ Oct 9, 2016 at 17:03
  • $\begingroup$ Well no. You just misinterpret the plot. If you use a revolutionplot for a given t, it'll look exactyl as in the image you provided. I update the post soon with a new plot. $\endgroup$ Oct 9, 2016 at 19:29
  • $\begingroup$ I have updated it. $\endgroup$ Oct 9, 2016 at 19:36
  • $\begingroup$ Okay, so what 'exactly' did you input to get this result. How did you type it in. I put $f(t,r)=(sin(r+t))/(t(r+1))^.1$ and got no graph whatsoever. $\endgroup$ Oct 9, 2016 at 22:39
  • $\begingroup$ I updated the post accordingly. There is also an animation for the wave. $\endgroup$ Oct 9, 2016 at 23:31

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