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Re: Impedance &c.



good show Leigh!

one of MY random questions on impedance, mulled over for some the years.

Electrical resistance of course is V / i ( or Z = E / j for the
sophisticates )

Power is (V) x (i.).

My question (suspicion) is:
are other impedances also going to be expressed as the ratio of an
intensive variable to an extensive variable - with the product of
these two variables being power???

a 'simple' system to analyze would be a spring loaded gun shooting a
projectile of mass m.

and what IS the impedance of a simple lever system?


There is a chapter on this very question in a wonderful little book
entitled "Similarities in Physics" by John Shive and Robert Weber.
(That's the same Shive that gave us the Shive Wave Machine, which has
become a staple in lecture demonstrations.) In general, if you
regard impedance as the ratio of cause to effect [and let's NOT get
into cause/effect arguments here], then in electrical circuits the
ratio would be the applied voltage to resulting current and the power
is their product.

For sound propagation, the impedance of an air column in an acoustic
tube, for example, would be the ratio of the driving force of the
sound-producing diaphragm or piston to the resulting velocity of the
layer of air adjacent to the vibrating surface and their product
would be the power.

Shive and Weber give examples from many areas, whether they be wave
physics or mechanics, etc. and talk about impedance matching devices
(transformers) in all of these situations for maximum transfer of
power. The book is a lot of fun.

-- Wolfgang

P.S.: In mechanics, the quantities transformed are force and
velocity and the transformer is the mechanical device (such as a
lever). The force exerted by the operator on the lever is stepped up
(or down) by the lever arm (transformer) ratios, but you pay for the
speed in a reciprocal manner. The power is again the product of the
force and velocity. In rotational mechanics, the analog quantities
are torque and angular velocity.