Re: [Phys-L] The resonance phenomenon in an open ended cylindrical tube

["John Clement" <clement@hal-pc.org>]

While true and accurate, the explanation will not work well with a beginning
student, except for the amplitude argument.  One could say that water is
"hard" and acts like a fixed end.  Very little energy will be transmitted by
the water.  But the pressure model may work better in an explanation.  As to
there not being properly a node at the water, that is a second order effect
and should be ignored in the initial simple model for resonance in pipes.
Students need to understand that models for phenomena are only tentative and
will be modified to cover small effects which are being ignored in the
initial model.

John M. Clement
Houston, TX 

> On 01/12/2015 11:10 AM, Savinainen Antti wrote:
> > The trouble is, she noted, that sound propagates faster in 
> water than 
> > in air. This means that there should be no phase change in 
> reflection. 
> > Hence, the incoming and reflected wave should not be out of 
> phase by 
> > half lambda to create a destructive interference (node).
>
>
> The wave equation in each medium is characterized by
> *two* numbers:  the speed of propagation and the impedance.
>
> The reflection from the boundary is characterized by
> *two* numbers:  the phase and amplitude.
>
> Reflection is controlled by the impedances, not by the 
> speeds.  This is super-easy to demonstrate with electrical 
> transmission lines.  You can have a piece of 50-ohm coax, a 
> piece of 75-ohm coax, and 300-ohm twinlead all with the same 
> speed of propagation.  There will be humongous reflections 
> from the interfaces.
>
>   There should be a way to visualize this with
>   mechanical waves but I can't at the moment thing
>   of a clean and easy way to do it.  The air/water
>   interface exhibits the effect but evidently doesn't
>   suffice to explain it.  Hmmmmm.
>
> Because of the extreme difference in impedance, the 
> transmission across the air/water interface has a very small 
> amplitude.  You can say whatever you like about the phase, 
> but it doesn't matter because the amplitude is so small.
>
> By conservation of energy or whatever, if the transmission is 
> small the reflection must be large.
>
> ===================
>
> As a separate matter:  Be careful about saying "there is a 
> node" wherever.  At an immovable boundary there will be a 
> node in the velocity but an /antinode/ in the pressure.
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