Wave Speed in Different Media

## Question:

May I have a question?

When a mechanical wave propagates from one medium to an other, let say the incident medium is of lower density and the medium, in which the wave was transferred is of higher density, i.e. a) air to to metal, or b) lighter spring fixed to the heavier one. Question: 1) Does the wave wave increase the speed, and the wave length as well, or 2) decrease both the speed and wavelength, or 3) decreases speed and increases wavelength?

I found all three responses to this question.

Thank you.

## Answer:

You might think of the situation you describe 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