It's been a very intense couple of weeks, and the stresses of running a business would be overwhelming if it was not for great music and passionate fans. However, it feels like the last two weeks have been filled by shoddy suppliers, intractable customers, and the final straw was 2 hours in a debate over the laws of physics....
So, here's another great use of the What's Best Forum - cartharsis. Instead of resorting to Angry Birds, I thought that I'd come back to something I enjoy and I've missed for the past 2 weeks.
We can debate endlessly about whether you can hear/perceive something, but the laws of physics are immutable. It is absurd to argue that electrons travel at or anywhere near the speed of light because if anything is accelerated towards light velocity, its mass increases, and the mass will approach infinite mass as its velocity approaches the speed of light. To accelerate electrons or anything else to anywhere near light speed would require huge amounts of energy, and would approach infinity as we approach light speed.
So, really, how fast does electricity travel?
Let's talk about electrical current - which is defined as the ordered movement of charge. The charge that moves in a liquid or gas (non-conductors) could be an ionic charge, but we are concerned about electrons in a conductor.
So, we can refine the question further by asking "how fast does an electron move in a conductor?"
The unit of current is the Ampere. One ampere is defined as one Coulomb passing a given point in a circuit in a second. The Coulomb is the unit of charge that is equivalent to 6.25 x 10^18 electrons. That's a LOT of electrons, but electrons are very tiny.
If we use copper as an example, copper has 8.5 x 10^22 atoms per cubic centimeter, and it has 1 mobile electron per atom. Since we know that the charge of a single electron is 1.6 x 10^-19 coulombs, we can easily work out the number of electrons that would need to flow past a point to have a single Ampere of current.
The formula is so simple that it is trivial:
V = I/(Q * e * R^2 x pi)
where V = velocity of electron in cm/sec
I = current in Ampere
Q = number of mobile electrons per cubic cm
e = electron charge
R = radius of conductor in cm (12awg has radius of 0.1cm)
V works out to 0.00234 cm/sec. That's 3.3 inches per day. The velocity of electrons is really slow.
If you're playing music at an average of 2 Watts into a pair of 8 Ohm speakers - that's 0.5 Amperes. An electron (let's call him Fred) that goes into a pair of 9-foot speaker cable will take 130 days for Fred to come out the other side plus a few more days to travel through the voice coil, inductors, circuit board traces, internal wiring, etc.
That's for copper. If the wire was silver, the electrons will flow slower. This is because both copper and silver have one free electron per atom, but silver is denser than copper, and therefore silver has more free charge carriers within the same cross section.
However, why then can we pass such fast signals for music over wires? This is because it's not electrons moving that we are talking about, it's because the electrons are already in the wire waiting to move. Imagine having a pipe that is completely filled with marbles. When an extra marble is pushed in one end, a marble almost instantaneousness drops out the other end no matter how long the pipe is.
The effect of electrical current is almost instantaneous (it cannot be instant) due to the domino effect of the electron charge carriers knocking on from atom to atom. Think of a row of dominos, with a gap in between. The larger the gap, the slower the knock-on effect.
So, now we change the question to "how fast does electricity propagate through a conductor?"
When the current flows, electrons move from atom to atom. As an electron is a charged particle, they have a force field (an electrostatic field or E-field). This field has a force associated with it, and a direction. So, when a current flows, there is an E-field radiating from the wire that flows with it.
Also, when the current flows, a magnetic field (the H-field) is generated around the wire. The force of the electromagnetic field has a strength that is inversely proportional to distance (like the E-field) but is circular around the wire (the direction is according to the right-hand rule).
When a current flows, the E-field and the H-field must rack together with the flow of current. No one field can get ahead and wait for the other to catch up. So, the issue is not how fast the electrons can move within the conductor, it is how fast the E- and H-field can travel in the medium it is travelling through (hence our interest in the dielectric around the conductor).
Electromagnetic fields travel at the speed of light when in a vacuum (unlike an electron which is a particle, fields have no mass). They travel almost at the speed of vacuum in air, but slower in any other medium. The difference in speed is inversely proportional to the square root of the relative dielectric constant.
For example, if the wire was insulated by water, which has a relative dielectric constant of 80, it will travel almost 9 times slower. Teflon has a dielectric constant of 2.1 - and hence will slow down the electrical propagation by 1.4 times.
If you had a pair of speaker cables, one insulated by air, and the other insulated by teflon, there is no way that you can hear the difference in the speed of the cable. Even if it was insulated by water, the difference is way below any hope of perception.
Light travels at about 300million meters per second.
There is no way to argue that a cable is "faster" or "slower" based on speed of electricity in a conductor.
So there..... better than therapy