Julius Sumner Miller: Lesson 31 - Waves - Kinds of Properties

A wave is a strange thing. Try to answer this question: What is a wave? It is not so easy to say. The best we can do for the moment is to say this: A wave is a disturbance which transmits energy. A better attack is this: let us show some waves and seeing what a wave does will tell us better what a wave is. This we call in Physics the operational point of view.

A - We have two rubber tubes - one called "empty" - the other filled with sand. I say "called empty" because it is really NOT empty. It has air in it! One end of the tube is fixed I hold the other end. Now by a slight blow with the hand I depress a bit of the tube and we see a pulse travel along the tube to the remote fixed end. This wave is a transverse wave - where the particle disturbance is at right angles to the direction of the energy propagation. If enough energy gets to the fixed and we might have a reflection. And we see the wave travel at a certain velocity. It I pull up on the tube and increase the tension the waves travels faster. With the sand-filled tube we see the wave velocity slower. It can be shown either experimentally or mathematically the velocity of a transverse wave is given by the expression V= T/m where T is the tension and m the linear density

B- We now show a different kind of wave with a spring called a SLINKY. Here we give rise to a pulse traveling along the spring in the same direction as the energy propagation. This kind of wave we call a compressional or longitudinal wave. Sound - we shall see - is a compressional wave mechanism.

C - With a piece of blackboard chalk we show a torsional wave by twisting the cylinder of chalk. Torsional waves are important - as in of a steamship shaft which delivers energy from the driving mechanism to the propeller - or in the drive-shaft of your car - where a torque is needed.

D - A dramatic showing of the propagation of a compressional wave arises in the collision of steel spheres on a track. One sphere strikes an array at rest. The compression travels with the speed of sound in steel - about 15,000 feet per second. Pretty fast !

E - Now transverse waves possess a special character: They can be polarized -just like light can be polarized. Compressional waves cannot be polarized.

F - Water waves are especially "tricky" business. They are made up of wave motions of several types but we understand these pretty well. The expression for the velocity of a water waves comes out
\
w _ ug x lambda 7 2 pi T
2 pi lambda x d
Which LOOKS awfully rough but really is not!

G - Conduction of sound energy requires a medium. And the more elastic the medium the greater the conduction. Thus it is that a metal rod conducts a compressional wave better than a rubber tube. And this is why a stethoscope works as it does. Look at one closely.

H - If sound is a compressional wave it needs something to compress if it is to be transmitted. Accordingly a bell in a bottle can be heard if there is stuff in the bottle - air - say — but if the air is pumped out no sound can be heard. So on the Moon - with no atmosphere - how will we hear each other?