It's 5200, the blue is 6000, and the red is 7300.

So what I've plotted here is this expression right here.

V out over Vs is really just this factor as a function of frequency, and so I've

plotted it from zero to 20 kilohertz, and the response is plotted from zero up to

three, so these are relatively low q. The pick-up on the peak at only about 2.2

or so. So these are fairly low q.

now the, in the first case, let's look at the blue case first.

It's two henrys, um,120 pico farads and about 60,000 Ohms.

So the resonant frequency is right around, 10 kilo Hertz.

If I take, and I increase, the number of turns, somewhat to 7,300, I can go from

two Henrys to three Henrys. The capacitance of, the interturn

capacitance of all of that, that coil of wire goes up some, and, so, the, the

resonant frequency drops, because l went up, and c went up.

So, if you go back here. The resonant frequency is one over the

square root of LC. And so if both L and C increase than the

resonant frequency drops. Now, I'm leaving the resistance the same

because there resistance is primarily due to the magnetic losses.

The loss of the wire itself, the resistance of the wire itself.

This may be only 10% of that. So it's not really critical to, to

reflect that in, in this model. But so if I go the other way and I will

reduce the number of turns then I decrease the inductants, the compacitance

goes down a bit. And the resonant frequency moves out to a

higher frequency. So this is how these three different

pickup configurations would correspond to the same driving signal.

Now the so What it says correspond to than in terms of what you here?

Well, there's a few few features to point out.

The first one is, if I increase the number of terms, then you make the

response of the pick up greater. It's actually it's greater at lower

frequencies, so the red curve is always above the other two curves below around

600 kilohertz and so you say that in that case this pick up is, is a hotter pick

up, it has a bigger output voltage. For the same amount of string motion.

So the blue is not as hot as the red and the green is less so than, than than

both. Now, the the other thing to point out is

that at frequencies above the resonant frequency, the, the green coil actually

has a higher response out at the very high frequencies than these other two do.

And so the, although the red has the greater number of terms, has a higher

response at low frequencies, the high-frequency response is less than the

blue or the green curves, than the, with the lesser number of turns.

And so, the high frequency overtones in the the string vibration, are not picked

up by the the red configuration as much as they would be by the, configurations

with lesser numbers of terms. So there's this trade-off between the

frequency response and, the, between really the low-frequency response and the

high-frequency response. You can get a greater output at the

expense of less response at the higher frequency, so you get a slightly darker

or not as bright sounding pickup. When people use the word bright to

describe tone, they're generally talking about the presence of high frequency

Harmonics or high frequency over tones in the, in the wave form.

So anyway, I think that's interesting to take a look at this example of the RLC

circuit in the guitar pickup and you can really now start to appreciate from our

simple model, exactly what the trade offs are for the number of turns and the size

of the output and the frequency response. But just one other thing to point out is

that this also is, is an example of a much more general type of resonant

circuit, and this is the same fundamental residence that is going on in the

mechanical systems that we looked at, masses on springs, but also the acoustic

systems. When we take a loud speaker and put it in

a cabinet. You can model the cabinet as a resonator,

and so we have, basically, coupled resonators, the loudspeaker and the

cabinet. And it's to, to complete the analysis of

that kind of a system, we need to understand how to compute the transfer

function of, of that com- that combined system.