Waves in a Struck Rod

## Question:

Hi. I have a few questions on waves, and I would appreciate your help.

1)If you strike a horizontal metal rod vertically from above, what can be said about the waves created in the rod?
a)The particles oscillate horizontally along the direction of the rod.
b)The particles oscillate vertically, perpendicular to the direction of the rod.
c)The particles oscillate in circles, perpendicular to the rod.
d) The particles travel along the rod.
I thought the answer would be choice (b) because the particles would oscillate up and down within the rod.

2) What is a wave and its function?

3)How are velocity, frequency, and wavelength affected in different mediums?

4)How do different mediums affect the behavior of waves?

I have read my class notes and text book to find the answers to these questions. I have a basic idea of how to answer them, but I would like further help. Thanks a lot, I appreciate your time and effort.

## Answer:

Here are some thoughts.

1. Striking a horizontal metal rod vertically from above is going to deflect the struck area downward. Inertia will prevent the entire rod from reacting downward at the same instant so the rod will be flexed with the struck point being low. The springiness of the rod will tend to straighten it but overshoot the initial straight condition, causing the struck area to go high relative to the rest of the rod. As you suggest you will end up with an up and down movement of the particles making up the rod. Depending on the length, stiffness and mass of the rod there may be one or more nodes along the rod's length where there is essentially no motion in the vertical direction while the rod on either side of these nodes move up and down.

That may not be the whole story, depending on the level of detail you look at. The up and down flexing motion in the rod is not totally isolated from motion along the rod's length. In real materials there is coupling between modes of oscillation so that some of the energy imparted to the rod will end up producing a longitudinal compression wave in the rod, essentially sound waves, running along the rod and reflecting from the ends. These waves involve motion of the rod's atoms back and forth horizontally.

It looks to me like answer b might be correct for an introductory course, and answers a and b correct for a more advanced course. Based on your next two questions it sounds like you are working a the introductory level.

2. A wave is a mechanism that transfers energy from place to place without necessarily any net movement of the transmitting medium. This somewhat awkward definition is general enough to cover waves of all sorts. A wave function is a mathematical expression which describes the progress of the wave both with regard to changes in space and time. For example a sinusoidal wave travelling down a string is described as f(x,t)=A*sin(2*pi*(x/l-t/T)) where x is the distance along the string, t is the time since the start of the observation, l is the wavelength and T is the wave period.

3. You might think of the situation in this way. At the boundary between the two materials the number of wave peaks per unit time exiting the lighter medium must equal the number of peaks per unit time entering the heavier medium since there is nowhere else for them to go and they can not be stored up anywhere. That means that the period of the waves in the two materials will be the same.

The speed of the wave front in the two materials will in general be different and will increase with the stiffness of the inter-atomic forces and decrease with the mass of the atoms. In the specific case of air and metal the net effect of all this is that compression waves travel faster in the metal. With a faster speed, the wave front will travel faster in the metal, covering more distance in the same period so the wavelength in the faster medium will be longer. The wavelength is just the speed of the wave times the period.

You know, it's like the two physicists who meet. One of them says "What's nu". The other says "c over lambda".

There are other interesting things going on at the boundary. For example some of the energy will be reflected back into the originating medium either with a phase reversal or not depending on the relative speed in the two media. As I indicated the speed is not strictly controlled by density but it tends to be higher in liquids that gasses and higher in solids than liquids.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ