Welcome back to Linear Circuits.
This lesson is going to be a lab demo on a
guitar string.
So, we're following up on the topic of
frequency spectrum with this experiment.
So, in the previous class, we introduced
the frequency spectrum
as a way of plotting the frequency content
of signals.
This lesson objective is to demonstrate
the use of a spectrum analyzer.
Well, this is a common measurement
instrument
for computing and displaying the frequency
spectrum.
And the guitar string is really a nice
experiment, because it produces a lot of
harmonics.
And you're able to see the different
harmonic
and the frequency content of, of a
particular signal.
So, our lab demo is guitar string
frequency spectrum.
This platform is a guitar string.
We have a pick up standard commercial
guitar
pick up, which is very similar to the
homemade guitar pick up that we saw before
when we looked at inductance and
applications of inductance.
The homemade one was just a coil of wire
around a permanent magnet.
So this one uses the same principle,
but it's has a better resolution to it.
And the guitar, our string is a steel
guitar string.
So, as you pluck the guitar string, it
vibrates inside the magnetic field
induced by this in, this guitar pickup,
and it causes a current.
So the current flows in through these
lines right here.
And then we're using this, this
dead acquisition board to just record
those signals, and we'll display the
signals.
So again, as I pluck this string
[SOUND],
I'm inducing electrical current.
Now, I want to look at this string, this
electrical current on a on a oscilloscope.
So if I look back at my oscilloscope here.
I've got this set to record from this
channel.
Now, let me go ahead and hit the guitar
string and we'll see what it looks like.
[SOUND]
And you can see a signal
that looks fairly
periodic, and it decays over time.
Let's go ahead and zoom in on this.
We definitely see something that looks
periodic, and that's what gives you the
tone that you hear from the guitar string,
but it's not a pure tone.
And this, this particular screen shot has
a lot of jaggedness
in there, and that's because the
resolution under which I recorded it.
[INAUDIBLE]
I changed the resolution,
and we'll record this again.
And we'll see it in a little bit better
resolution
There we go.
Alright.
So, rerunning this with a better
resolution.
Let me go ahead and zoom in on it a little
bit more.
And we can see, this is what a
guitar string vibration looks like when I
pluck it.
If I look at this, I see definitely a a
fundamental frequency.
From here to here is the fundamental
period, that's the basic tone that
you've got.
That's the basic note in other words.
But I also see some things happening in
the middle.
In fact, I see a dip right here, about
half way.
So a dip, I see a dip here, a dip about
half way and a dip here.
And that dip halfway corresponds to a
second harmonic.
So, it's another frequency in there.
And then if I look at this, I see a peak
right here.
That's about a third of the way, that's
really
a third harmonic.
And then we actually see a fourth harmonic
here as well.
So I see multiple harmonics in this
signal.
Now, to analyze this a little better, it's
easier to look at a
[UNKNOWN]
dynamic spectrum analyzer.
Going back to the platform here.
A dynamic system, a dynamic spectrum
analyzer
is accomplished by taking your recorded
signal,
feeding it into a data, data acquisition
board and then you record that signal.
Now I'm going to put the, that instrument
up here.
And let's go ahead and run this.
The dynamic spectrum analyzer takes the
recorded signal and performs a
fast voyage transfer on it in order to get
the frequency spectrum.
And what you see plotted here is the
magnitude in decibels versus frequency.
And the frequency is on a linear scale.
But once we put something into decibels,
it is actually a log scale.
Because to compute the decibels,
magnitude in decibels, we take 20 times
the log of the magnitude.
Now, what we see here is that there's a, a
little bit
of a peak right there and I have not yet
played a note.
So, it's curious to see where that peak
occurs.
May I turn my cursor on and go ahead
and slide it across to see where the peak
occurs.
It occurs right there.
And if I look at that frequency, that is
at 60 hertz.
Now, it's very, very common to get noise
at 60 hertz.
This is electromagnetic noise.
And it's induced by power lines in the
room.
it could be induced by vibrations from
equipment,
which is powered by 60 hertz power lines.
So, in this country the line current
is at 60 hertz.
So, we see 60 hertz signals in noise and
signals.
In other countries, you might have 50
hertz and
then therefore your noise would be at 50
hertz.
But that peak there has nothing to do
with our experiment, so we're going to
ignore that.
That 60 hertz peak in our experiment.
We're just going, looking at the peaks due
to plucking this string.
So, if I pluck this string again,
[SOUND]
what I see are all these peaks.
This is the
fundamental frequency that we saw in our
time trace.
This is the second harmonic, the third
harmonic.
And in this case, the second harmonic is
almost
as strong as the first harmonic, a little
bit lower.
And let's go ahead and measure what that
frequency is.
I turn my cursor on,
slide this across.
It's,
that's as
close as I can, it's around 440 and that's
an A note.
Now, what we're seeing is that we've got
our A note.
And then we've got our higher harmonics,
and that's
what gives the richness of sound in a, in
music.
In most
musical instruments, they rely on the
harmonics
to give it the richness of the sound.
So in this case, we've looked at the,
we've looked
at the application of the frequency
spectra in order to analyze the signal.
We will be using this experiment later
when we go on to filtering.
You might say, what if we don't want to
hear that second harmonic?
What if we wanted to get rid of the, the
60 hertz signal?
And so, we want to use this experiment
later for filtering.
The basic concepts that we've covered
though, were
to look at the dynamic spectrum analyzer
and
to look at the frequency res, frequency
spectrum that we get out of a real signal.
Thank you.
So in summary, the Dynamic Sys, Spectrum
Analyzer
is an instrument to measure and compute
the frequency
spectrum of measured signals.
The guitar string is a great platform.
Because it produces all kinds of frequency
content and harmonics in there.
And we can look at the fundamental
frequency and
we can look at those harmonics, and
measure them.
We will see the, this experiment later on,
when we get to the topic of filtering.
So,
in the next lesson, we will combine the
transfer function concepts with the
frequency conc spectrum concepts in order
to
determine the frequency response of a
circuit.
I will see you online, and I hope that
you go to the form and ask and answer
questions.
Thank you.