🚀 go-pugleaf

On Fri, 5 May 1995, David J. Abineri wrote:

> Another high school physics question that I had a hard time answering.
>
> Look at a standing wave on a slinky. The nodal points are stationary. How does
> the disturbance get from one side of a nodal point to the other if that point
> isn't able to move?  It would seem that any disturbance would be stopped when
> it reaches a node.

What's there to stop it? To make a *very* crude analogy: When a ball is
thrown straight up, it is momentarily at rest at the top of the
trajectory. Does the ball therefore stop there? No. A defect of this
analogy is that the ball is a material object. Your wave isn't.

> If two congruent pulses are sent on Opposite sides of the spring
> simultaneously they cancel exactly at one moment in time. Is there any way to
> know whether, after that instant, the waves continue in the same direction
> they were moving or in fact "bounce" off each other and return to their
> respective starting ends.

Part of the problem is treating the 'wave' as if it were a 'thing'. It is
merely a mathematical description of the position of the parts of the
medium (the spring), or, if you like, a mathematical description of the
velocity, or the tension in the spring (or the pressure in a fluid
medium) etc. None of these are 'things' in the sense that a material
object is a 'thing'.

A related problem dates back to the ancient Greek thinkers. If you push on
one end of a stick or rod, what causes the whole rod, and the other end,
to move? Also, if the other end moves, does it do so instantly? No, just
as in the spring, a compression occurs at the pushed end, causing a
compression pulse toward the other end, moving at the speed of sound in the
rod. Now consider hitting the rod with a hammer. A standing wave is set up
in the rod, with nodes and antinodes. The pressure pulse can propagate
right past a node, in fact, to a first approximation its speed of
propagation is the same whether moving through nodes antinodes or
anything in between, so long as the amplitude isn't so great as to exceed
the linear region of elastic response of the medium.

This is another case where one gets in trouble trying to understand an
essentially calculus concept with a non-calculus 'explanation'. (The tide
problem was another example.) The pressure pulse in the spring is related
to the derivative of the motion of the particles of the medium. So at that
node you spoke of, there can be a region of compression centered on the
node (even passing through it) while exactly at the node there's one
(or many) particles which are not moving.

        -- Donald