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

[John Denker <jsd@av8n.com>]

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.