James9118 wrote:
Let's take this picture and discretise it, i.e. imagine at the exact point in time pictured, an infinite number of scissors cut the line into particles, we can then track the motion of these individual bits.
This hypothetical situation gives a nonsensical answer. Transverse waves require both mass and tension: cut the medium into small pieces to provide discrete masses and you remove the tension. It is impossible to transmit a transverse wave through disconnected points. The motion of each individual bit relies on being connected to the individual bit it is pulling through space
and the bit it is pulling.
In contrast if I discretise a fly cast, at some point during the stroke (let's assay it's going left) then it all moves off at the same velocity (it has to otherwise we'd see the line stretching).
That is beside the point of this because, yes, the fly line does stretch when we apply a force to it. The largest stretch is at the rod tip because that point is pulling the most mass. You're not proving anything by implying the line does not stretch.
I'll go back to your two hypothetical experiments: performing the video in zero gravity and casting vertically.
As you probably know, a lot of physics 'takes place' in space with no gravity - what happens to your transverse wave there? (It makes no difference to a true transverse wave).
Also if I lean out of a tall building and cast vertically up and down, what happens to your transverse wave then? (Again this makes no difference to a true transverse wave).
I was thinking more on these last night and the questions themselves (and their answers) give me an insight into why you're so against the cast being a transverse wave. The answers you'd like me to give you are:
1: In zero gravity, the line being cast back and forth will ultimately occupy the tip path when the fly is not tethered, and
2: When the cast is performed vertically, the line will occupy the tip path and the line crashes into itself.
These two hypothetical conditions have one thing in common: zero tension. Tension is a requirement for a true transverse wave, and that tension must be perpendicular to the displacement vectors.
- waves_T.jpg (22.06 KiB) Viewed 3273 times
For a transverse wave to propagate, two conditions must be met. There must be tension in the medium and the medium must have mass. With those, we can calculate the velocity of propagation of the wave as V = sqrt(Tension/Mass per unit length). The direction of propagation (shown above) is
always in the orientation of the average tension vector, here being the "upright" of the red T. Displacement of the particles is in the direction of the cross of the T. Of course, the T is on its side, but I'll use the T as a frame of reference.
Pretend I went into space and took my fly rod. I
also took a piece of rope and found a place to tie it to.
I conducted the experiment as asked, oscillating the tip along the cross of an imaginary T with the line laid out on the upright. The fly line pulled towards me and I got line tangled around the rod tip. With none of the tension from the gravity I had on Earth, the fly line occupied the tip path and I tangled up. There was no tension in the upright of the T, so the wave could not propagate along the upright towards the bottom of the T.
I then set my rope up as above and moved it sideways. With the rope (and me) tethered, a wave was propagated along the rope towards the tether. Then the pissed off cosmonaut who was with me cut the rope at the tether and the rope eventually pulled towards me and tangled up in my hand. Tension was lost and my transverse wave collapsed into the same state as the fly line did.
The reason the video of mine shows a transverse wave with the direction of propagation being vertical is that
gravity provides the necessary tension in the line. Rather than "an unusual set of conditions" (your objection), these are the mandatory conditions required for a transverse wave. Tension and line mass.
The reason your vertical cast provides unsatisfactory results is that the displacement of the line (particles)
must be perpendicular to the tension vector. Gravity can only provide tension downwards, so we can only make a transverse wave in the line by moving the tip horizontally. Hanging a rod out the window and casting up and down doesn't work unless the fly line is tethered to the building across the road to provide tension (exactly as shown in the Waves_T picture above).
James wrote:Do you see that you're now being inconsistent, in the above statement you're relying on gravity to achieve the vertical propagation. Remove gravity (or cast vertically) and now you have no propagation perpendicular to the displacement
Do you now see that gravity is
absolutely necessary to achieve a vertical propagation orientation? Gravity provides the tension vector required for a transverse wave to propagate in an untethered fly line. As you say, remove gravity and there cannot be propagation, the corollary of which is "apply gravity and there
must be vertical propagation when the displacement vector is horizontal."
Another question you asked is how can this be used to further the understanding of casting. I'll deal more with it later, but one application is explaining why too much overhang is a problem (v=sqrt(T/mass): as mass approaches zero, infinite velocity is required for the wave to propagate into a heavy medium) and another is why a blown anchor fails in a spey cast (T approaches zero). It also helps explain why line tapers work (T and mass
both approach zero) . I'm sure there are others ....
Cheers,
Graeme