this is some extra discussion following
our main video about phil's homemade
radio
right what we've got so over here
we have this wonderful crystal radio now
we covered a lot of the physics but one
thing we didn't really focus on because
there's an awful lot even though this is
just a few components this is there's an
incredible amount of physics and
electronics going on in this the core of
this as well as the diode is what's
called a tuned circuit so when i adjust
this
so nothing now what i'm doing is i'm
changing the capacitance
and that's changing what's called the
resonant frequency of this circuit the
frequency at which it's most sensitive
resonance is absolutely crucial across
all physics
and all engineering it's it's first
second third year or undergraduate
post-graduates right across the board it
crops up time and time again from
everything from pushing somebody on a
swing
or a mass on a spring i like this monkey
bumping up and down at a particular rate
at its natural or resonant frequency and
that's set in this case by the stiffness
of the spring and the mass of the monkey
it's a very simple equation
similarly here what we're doing is we're
choosing a particular
frequency out of a range of frequencies
this particular station broadcasts at i
think something like i forget this wrong
absolute radio i apologize but it's
something like 1.2 megahertz so 1.2
million times a second the the radio
wave is moving back and forth but this
red this wire by itself isn't just
picking up that signal it's picking up
all the other signals as well so what
you need to do is is is to narrow in and
get that frequency which is what was
happening earlier wonderfully we've got
a mechanical we can see this idea of
resonance really straightforward this is
a very simple setup we've got a bar a
ruler basically and it also has its own
natural frequency we're actually going
to drive it mechanically there's a
solenoid here and there's a magnet so
we're just driving it back and forth
with a magnet and to monitor the motion
we could look at this but we're going to
do something even nicer which is we've
got a laser pointer that's quite neat
because what we have is something that's
going to tell us just how much this is
vibrating so what's happening is the
laser going down down and there's a
little mirror and then just bounce
around okay at the moment you can see
it's bobbing up and down but not very
much no so we're at four hertz 4.4 hertz
brady so what i'm gonna do is i'm gonna
turn the frequency up notice i'm not
driving it the amplitude stays the same
all i'm changing is the frequency this
is really important and okay so it's
going up it's going up and of course the
frequency is going up so it's bouncing
around a little bit more 12 hertz 14
hertz 15 hertz okay so we're getting
some but not much
16
17 18 now a little bit more but not much
still so that's not much more than when
we were at four hertz that's off
resonance right so we haven't hit the
natural frequency remember we had the
monkey and how did so what i'm going to
do is find the natural frequency see it
building up oh yeah right so we're at to
resonant frequency right now if we go
the other side of what happened why is
that thing suddenly going yeah i'm going
crazy because what you've done is
exactly what the radio circuit is you're
driving it with the right frequency it's
got its own natural frequency just as
the monkey on this thing or any mass on
a spring has its own natural frequency
this has its own natural frequency and
now you're driving it at that natural
frequency and what is that frequency and
our frequency is about 25 hertz the
difference is is when you're away from
that frequency you don't get much energy
transfer so it's still vibrating but
when you hit that resonance resonant
frequency that's where you get a lot of
energy transfer into it and it actually
acts as a filter because if we go above
that we're now at 33 hertz
but now we're the other side and it's
staying off and you can see that it's
reduced almost to what it was when we
were at 18 hertz so you're saying when
you put in the correct
natural resonance frequency energy
transfer like does that mean it's kind
of like to use a term you probably won't
like it's almost like the stars have
aligned and this is like yeah the way
all my structure works and my length and
my what i'm made of this is just the
perfect thing for everything precisely
you can do this experiment without
driving it this
ruler its resonant frequency depends on
its length so if i make this long
relatively low resonant frequency if i
make it short
higher resonant frequency you can even
hear the note
changing
resonant frequencies going down and it's
so if i took this now when i drove it at
that frequency i get a lot of energy
transfer and you'll get this big
response
that's what's happening here but it gets
better so we can draw a parallel between
what's here and what's here
so here we've got a mass
and we've got uh
some friction and that's you know
friction due to the rod itself but also
with the air and we're driving it with
this and what we also have is some
stiffness because the ruler's got some
stiffness over here
we've got inductance capacitance it's
being driven by this by the the radio
waves and what's absolutely remarkable
is that the inductance here if we write
down the equations i'm not going to do
that don't worry brady but if you write
down the equations what we find is that
we can do a one-to-one mapping of
inductance to mass
capacitance to spring constant to
stiffness also in terms of the driving
force in this case it's a mechanical
driving force in this case it's an
electrical driving force and the
equation that the differential equation
you write down is identical and the
solutions are identical so that's why
you see resonance here and you also see
resonance here at different frequencies
but it's the same phenomenon so that
moment when you got that bar to jump up
and down like crazy there is the same as
the moment when you got absolute radio
exactly perfect
black or dark red this highest point is
going to be white and then scale it or
we can do what we're doing here and we
can listen to it