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.
Everything stands and falls with $\delta$.
With $\delta<0.5$ every value of $\alpha,\beta,\gamma$ seems to work fine.
Here you have $\alpha=1,\beta=1,\gamma=1,\delta=0.1$
As a revolutionplot with fixed $t$
With a dynamic updating t: $0.2\leq t\leq 10$. Interestingly, the time direction seems to have the wrong sign.
And explicit for OP a string for $t=1$ for Wolfram|Alpha