- #1
alingy1
- 325
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My teacher assigned me to prove open-closed and closed-closed standing waves patterns using math.
With closed-closed, it was fairly easy:
$$\begin{align}
D(x=0,t)&=0\\
D(x=L,t)&=0=2A\sin(kx)
\end{align}$$
Isolate $$L$$ to find that $$\lambda=2L/m$$.
Similarly for closed-open.
$$\begin{align}
D(x=0,t)&=0\\
D(x=L,t)&=\pm 1=2A\sin(kx)\\
\lambda&=4L/m.
\end{align}$$
I wanted to prove open-open too. But I am stuck.
I know that:
$$\begin{align}
D(x=0,t)&=2A\cos(\omega t) \\
D(x=L,t)&=2A\cos(\omega t).
\end{align}$$
Where do I go next?
With closed-closed, it was fairly easy:
$$\begin{align}
D(x=0,t)&=0\\
D(x=L,t)&=0=2A\sin(kx)
\end{align}$$
Isolate $$L$$ to find that $$\lambda=2L/m$$.
Similarly for closed-open.
$$\begin{align}
D(x=0,t)&=0\\
D(x=L,t)&=\pm 1=2A\sin(kx)\\
\lambda&=4L/m.
\end{align}$$
I wanted to prove open-open too. But I am stuck.
I know that:
$$\begin{align}
D(x=0,t)&=2A\cos(\omega t) \\
D(x=L,t)&=2A\cos(\omega t).
\end{align}$$
Where do I go next?