Question: This question has been bothering me for a very long time.

Imagine a wire carrying electric current. It carries two alternating current (AC) signals of different frequencies (say $50$ Hz and $60$ Hz). Now, since both the signals are on the same medium (wire), if I see the resultant signal on an oscilloscope or other device, I would actually see a new resultant signal that is an algebraic sum of individual waves at every point, but not the original signals anymore. 

How can the individual signals (waves) be separated from the wire after they combined to form a new wave? I know the telephone lines and TV cables carry multiple frequency signals on the same medium, and we successfully separate them at the receiver, but was thinking how is it possible to separate out individual signals when they combine and result in a different wave altogether? How can receiver figure out the original two waves or hundreds of waves that resulted in the combined wave?

I read about Fourier series analysis and signal filters but it just does not make sense fundamentally to me.

It is like adding two numbers 2 and 3 which results in 5 and being able to separate them again in to 2 and 3 and not 1 and 4 or some other combination. The medium (wire) has only the combined superimposed wave. How does the receiver know that 5 should be separated as 2 + 3 but not 1 + 4 or 2.5 + 2.5
I hope I'm making sense. I tried googling this but I think I'm not framing the right search terms.

Answer: 
It's not the pipe that's affecting the discharge speed. The only thing that matters in these equations\* is **the height of the water column above the hole**.

The water at the opening in B has more water pushing down on it from directly above, so it makes sense that it should exit faster. But the fact that there's a pipe surrounding the column doesn't actually matter. To show this, suppose we construct a tank C, which looks the same as tank A (i.e. no pipe) but has a height $h\_1+h\_2$. If you use those same equations, you'll find that the water exiting the hole in the bottom of tank C (with no pipe) has the same velocity as the water exiting the hole in the bottom of tank B (with a pipe).

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\*Note that these equations are themselves a simplified model of the way actual fluids work. In particular, they're only reliable for completely inviscid liquids (i.e. those that flow without any internal resistance).
I suspect that the velocity of fluid flowing from a container through a hole is $\sqrt{2 g h}$ only if the area of the hole is much smaller than the cross-section area of the container, otherwise the pressure cannot be maintained at the hole. Imagine that in case A the entire bottom falls out from the container, then the liquid will not move with the velocity of $\sqrt{2 g h}$. Case B is similar to that: the tube has no bottom.

EDIT (9/2/2019): See <http://www.physics.princeton.edu/~mcdonald/examples/leaky_tank.pdf> : " the velocity V of the eﬄuent stream from the tank is a function of the area ratio $a/A$", where $a$ is the area of the hole and $A$ is the cross-sectional area of the tank.