You can simulate a transmission line with lots of series inductors and parallel capacitors, but that is a lot of trouble and I'm not sure will give you the insight you really want.
It's actually not that hard to see obvious transmission line effects at high frequencies if you have a oscilloscope. If your electronics club doesn't have one, that would be a great piece of equipment to ask for. In the mean time, find some company in the area that does electronics and is willing to help out high school students. I suspect most of them would be happy to help if asked.
We did this in a lab in college, and I remember being surprised how clear and obvious the results were. Get a spool of some cable. Coax would be great, but 100 feet of ethernet twisted pair cable will work well too. Most likely whoever handles the network in your school has a spool of "CAT5" or similar cable they can let you borrow.
Use a signal generator or a simple circuit with a digital output that makes a square wave. Connect ground and this square wave to one end of a twisted pair, and get access to the other end of the same twisted pair.
First just look at the signal as injected at the transmitting end with and without about a 50 Ω resistor in series. Especially with the resistor, you should be able to see stair steps as the reflection from the other end gets back to the transmitting end. Now you can put a 50 Ω resistor accross the far end and see the effect it has on the transmitting end. Also look a the signal at the far end with and without each of the resistors in place. I think you'll see clear artifacts from the reflections, and how things quiet down but are half the voltage with the resistors in place.
Other things to do is to adjust the resistors for minimal ringing, which means finding the characteristic impedance of the line. It would also be a interesting exercise to measure the total propagation time thru the cable, measure the length of cable, and compute the actual propagation speed on that cable. You may be surprised what you find.
Reflections happen everywhere, not just in transmission lines. Transmission line is a model of the physical situation, which is easy to apply to a pair of conductors whose length is comparable to or larger than the wavelength of the signal, and which is regular in cross section.
What determines whether reflections matter is the frequencies in and the physical size of the circuit. If you have unmatched impedances then you do get reflected waves just as you describe, and either you have to deal with them or they are negligible for some reason. Here are two reasons:
For exclusively low-frequency circuits, the reflections reflect repeatedly and settle down on a timescale much faster than the signals change. That is, each double reflection is an extra signal which is merely out of phase with the original signal, but as they get more out of phase their amplitude drops quickly enough that they can be neglected. (Even RF circuits can be built this way, as can be seen from a lot of homebuilt HF amateur radio gear.)
As frequency increases, wavelength decreases, and the physical size of your components becomes relatively larger, and you start having to worry about avoiding impedance “bumps”. This is where you start using microstrip design techniques in printed circuits.
In digital circuits, sharp transitions may have high-frequency components that will reflect but you don't have to worry about this as long as your clock speed is much slower than the length of your traces/wires (there's a conversion via c to make that make sense, of course) because by the time the clock makes its next tick all the signals have settled down to a steady state.
(Note that there are no standing waves here because within the period of a single clock tick the driving signals are steps (high to low or low to high logic levels), not periodic signals.)
As clock speed increases, the settling time available decreases, requiring you to either minimize reflections or minimize signal travel time (so that the settling occurs faster).
Best Answer
The following figure gives you an idea which stability is to be considered based on transmission system voltage level and length. Since Thermal limit is fine, I will give a brief idea about voltage stability and rotor angle stability.
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Let us take the following simple single load-infinite bus system
The active/reactive power received by the load is given by,
\$P=-\frac{E V}{X} sin(\theta)\$
\$Q=-\frac{V^2}{X}+ \frac{E V}{X} cos(\theta)\$
After doing some math you can get the receiving voltage relation with the system parameters and load condition as follows,
\$V=\sqrt{\frac{E^2}{2}-QX\pm\sqrt{\frac{E^4}{4}-X^2P^2-XE^2Q}}\$
By plotting PV curve for different power factor of load we can get,
Where \$tan \phi=Q/P\$.
Note the following points,
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Assuming you have the same previous system but with connecting a synchronous generator instead of load. The active power transfer between the synchronous generator and infinite bus is given by,
\$P=\frac{EV}{X}sin(\delta)\$
Where \$\delta\$ represents rotor angle (load angle in some references). If we plot \$(P,\delta)\$ for different generator terminals we get,
P1 in this figure represents mechanical power of generator (power set point). The intersection between P1 and (\$P,\delta\$) curve represents the operating point of the generator. Now as long as the operating point is such that \$\delta\ <90^\circ\$, the system is stable. When \$\delta\$ cross the \$90^\circ\$ limit the system becomes unstable. Note the impact of generator terminal voltage on improving the stability.
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Note that this is very basic idea about stability issues, it is more complex in reality. So it is recommended to read further if you are interested in this topic.