Phase Velocity

Can somebody explain phase velocity to me. There is an entry in 
Wikipedia but it is a little confusing.

http://en.wikipedia.org/wiki/Phase_velocity

They have what looks like a double sideband suppressed carrier waveform 
and seem to suggest that it is the envelope that is the phase velocity? 
Apparently the phase velocity can be faster than the waveform itself. As 
an EE normally the carrier is a higher frequency than the envelope...


F

fitlike <naespamboy@scotland.co.uk> wrote:
> Can somebody explain phase velocity to me. There is an entry in 
> Wikipedia but it is a little confusing.

> http://en.wikipedia.org/wiki/Phase_velocity

> They have what looks like a double sideband suppressed carrier waveform 
> and seem to suggest that it is the envelope that is the phase velocity? 
> Apparently the phase velocity can be faster than the waveform itself. As 
> an EE normally the carrier is a higher frequency than the envelope...

When I learned it, phase velocity was w/k, group velocity dw/dk,
where w (omega) is the angular frequency and k the wave number
(or wave vector in more than one dimension).  (w is 2pi over the
time period, k is 2pi over the spatial period.)

But no, the envelope travels at group velocity and, in the usual
case, is where the information travels.  Phase velocity is often
faster than c, where group velocity should be less than c.

One example uses a Gaussian envelope which is a good representation
for a quantum mechanical (with uncertainty) particle.  

In DSP context, phase delay and group delay are more usual,
but they are related.

-- glen

On Aug 10, 12:58&#4294967295;am, fitlike <naespam...@scotland.co.uk> wrote:
> Can somebody explain phase velocity to me. There is an entry in
> Wikipedia but it is a little confusing.
>
> http://en.wikipedia.org/wiki/Phase_velocity
>
> They have what looks like a double sideband suppressed carrier waveform
> and seem to suggest that it is the envelope that is the phase velocity?
> Apparently the phase velocity can be faster than the waveform itself. As
> an EE normally the carrier is a higher frequency than the envelope...
>
> F

This is very confusing material, that really requires
you to contemplate. With a not insignificant risk of
your going crackpot.

Have a look at bow waves off ships or boats. The wave
fronts internsl to the wave train propagate at phase
velocity; the wave front travels at group velocity.

Rune

On Aug 10, 10:09&#4294967295;am, Rune Allnor <all...@tele.ntnu.no> wrote:
> On Aug 10, 12:58&#4294967295;am, fitlike <naespam...@scotland.co.uk> wrote:
>
> > Can somebody explain phase velocity to me. There is an entry in
> > Wikipedia but it is a little confusing.
>
> >http://en.wikipedia.org/wiki/Phase_velocity
>
> > They have what looks like a double sideband suppressed carrier waveform
> > and seem to suggest that it is the envelope that is the phase velocity?
> > Apparently the phase velocity can be faster than the waveform itself. As
> > an EE normally the carrier is a higher frequency than the envelope...
>
> > F
>
> This is very confusing material, that really requires
> you to contemplate. With a not insignificant risk of
> your going crackpot.
>
> Have a look at bow waves off ships or boats. The wave
> fronts internsl to the wave train propagate at phase
> velocity; the wave front travels at group velocity.
>
> Rune

For small boats, this is easier to observe in the wake. Close
examination reveals that individual waves arise at the inner part of
the vee, move to the outer part, then decay. the individual waves
therefore travel faster than the vee as a whole.

Jerry
--
Engineering is the art of making what you want from things you can get.

Rune Allnor <allnor@tele.ntnu.no> wrote:

(snip on phase velocity)

> Have a look at bow waves off ships or boats. The wave
> fronts internsl to the wave train propagate at phase
> velocity; the wave front travels at group velocity.

I haven't thought about this one for a while.  As with another
recently asked question, and without looking at Wikipedia, 
which quantities would you expect the angle of a bow wave
(relative to the boat direction) to depend on?

a) The speed of sound in water (or other liquid)
b) The viscosity of the liquid (which might not be water)
c) The depth of the liquid
d) The local gravity (small g)
e) The speed of the boat

(Note that the phase velocity of surface waves depends on
two of the quanities listed above.)

Also, liquid surface waves are an interesting case for phase
velocity, as the phase velocity can depend on wavelength.

-- glen

On Aug 10, 8:40&#4294967295;pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote:
>
> (snip on phase velocity)
>
> > Have a look at bow waves off ships or boats. The wave
> > fronts internsl to the wave train propagate at phase
> > velocity; the wave front travels at group velocity.
>
> I haven't thought about this one for a while. &#4294967295;As with another
> recently asked question, and without looking at Wikipedia,
> which quantities would you expect the angle of a bow wave
> (relative to the boat direction) to depend on?
>
> a) The speed of sound in water (or other liquid)
> b) The viscosity of the liquid (which might not be water)
> c) The depth of the liquid
> d) The local gravity (small g)
> e) The speed of the boat
>
> (Note that the phase velocity of surface waves depends on
> two of the quanities listed above.)
>
> Also, liquid surface waves are an interesting case for phase
> velocity, as the phase velocity can depend on wavelength.
>
> -- glen

All of the above? I remember I used this example
when i attempted to wrap my mind around these
concepts ages ago. Very visual. Very useful.

Rune

On Aug 10, 2:40&#4294967295;pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> Rune Allnor <all...@tele.ntnu.no> wrote:
>
> (snip on phase velocity)
>
> > Have a look at bow waves off ships or boats. The wave
> > fronts internsl to the wave train propagate at phase
> > velocity; the wave front travels at group velocity.
>
> I haven't thought about this one for a while. &#4294967295;As with another
> recently asked question, and without looking at Wikipedia,
> which quantities would you expect the angle of a bow wave
> (relative to the boat direction) to depend on?

The wake angle depends on the velocity of surface waves (which depends
on depth and g) and on the speed of the boat. The effect (and
equations) are the same as for hypersonic passage through air. Below
the wave speed, i.e., "tranquil flow", there is no wake.

  ...

Jerry
--
Engineering is the art of making what you want from things you can get.

Jerry Avins <jya@ieee.org> wrote:
(snip, I wrote)
>> I haven't thought about this one for a while. &#4294967295;As with another
>> recently asked question, and without looking at Wikipedia,
>> which quantities would you expect the angle of a bow wave
>> (relative to the boat direction) to depend on?

> The wake angle depends on the velocity of surface waves (which depends
> on depth and g) and on the speed of the boat. The effect (and
> equations) are the same as for hypersonic passage through air. Below
> the wave speed, i.e., "tranquil flow", there is no wake.

So when a boat goes twice as fast, the wake angle is reduced
by (about) a factor of two?   Sounds good, but compare the wake
of a duck to the wake of a ski boat.   The ski boat might go 50mi/h,
the duck maybe 1mi/h.  Or just watch the ski boat at different speeds.

-- glen

fitlike <naespamboy@scotland.co.uk> wrote:
> Can somebody explain phase velocity to me. There is an entry in 
> Wikipedia but it is a little confusing.

> http://en.wikipedia.org/wiki/Phase_velocity

To continue the discussion about boat wakes, and get back to
phase velocity, see the page:

http://en.wikipedia.org/wiki/Wake

The dispersion relation for deep water waves is w=sqrt(g k) 
where w is the angular frequency (radians/sec), g is
the acceleration due to gravity (m/s**2), and k is the wave number
in radians/meter, that is, 2pi/wavelength.

For deep water waves, depth greater than about half the wavelength,

the phase velocity is then w/k = sqrt(g k)/k = sqrt(g/k) 

the group velocity, dw/dk, or sqrt(g/k)/2.

The wake angle is then arctan(Vp/Vg), (Phase velocity/group velocity)
which is arctan(1/2), or about  26.5 degrees.

As to the original question regarding DSB-AM modulation, the
phase velocity is the velocity of the carrier, the group velocity
of modulation to the carrier, assuming it is sufficiently slow
relative to the carrier itself.

Consider a wave with a Guassian envelope.  There is a combination
of pure sines that add up to such localized wave packet.

If you look closely at the wake, you will see that it is a sum,
or interference pattern, of a range of wavelengths (and frequencies).

For real boats, the boat shape has some effect on the wake,
but the angle doesn't get far from arctan(1/2) in most real cases.
That is, independent of boat velocity, viscosity, g, density, etc.

-- glen

On Aug 11, 5:21&#4294967295;am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:

  ...

> For real boats, the boat shape has some effect on the wake,
> but the angle doesn't get far from arctan(1/2) in most real cases.
> That is, independent of boat velocity, viscosity, g, density, etc.

Wow! I need to dust off some old texts and straighten myself out.
Thanks for the start on that.

Jerry
--
Engineering is the art of making what you want from things you can
get.