why does a mechanical wave travelling from one medium to another preserve just its frequency?

Question

Previous answers to this question revealed to be completly unsatisfactory. No one was able to explain why the frequency, being a characteristic of the source, preserves itself when the wave passes from a medium to another one.

it is well known that the propagation velocity V (a characteristic of the medium), the wavelenght L and the frequency F are related by V=LF. But changing the V, only L will change. Why can't the frequency change instead, or why can't change both?

Answer 1

Skimming through the replies, I see the source of your dissatisfaction. The answers tend to be tautological (boiling down to "it is because it is"), or that some theory said so. It's really more basic than that. To answer your question correctly, though, we'll need to add some qualifications, because there are indeed some cases where it's not true.

First, we need to assume we're talking about a continuous elastic medium or an assembly of connected elastic media (like real springs wound from elastic material). Assume the source at P0 to have a constant frequency F0 for a sufficiently long time to propagate its effect to all points of interest so as to settle down into a steady state for as long a time as we wish to consider. Assume also that some remote point P1 is oscillating at frequency F1. Now trace an arbitrary path between P0 and P1 without leaving the medium anywhere along the way. Over any time period T, P1 transmits T*F0 wave crests while P1 receives T*F1 crests. The number of wave crests (surfaces of maximum displacement) intersected by the path will therefore have T*(F0-F1) more crests at the end of the interval than it did at the beginning. However, our steady state assumption implies that the number of crests along the path must remain constant. Therefore, F1=F0. Any other answer will result in waves bunching up along the path or rarifying as time goes on.

Answer 2

Try the following: Get a tall glass, fill it halfway with water and the other half fill with cooking oil (the cooking oil will float on the water right away if you pour it slowly). Drop small pebbles (or some other dense item) into the glass at a frequency of 2 per second. Once the first pebbles hit the bottom, have someone else time how frequently they hit the bottom. Your partner will measure the same period with which you are dropping the pebbles, hence the same frequency.

The pebbles leave your hand (the source) at a frequency of 2 Hz. Once the steady state condition is set up, they hit the bottom with a frequency of 2 Hz. So the frequency of the rocks travelling thru the oil is the same as the frequency when it travels through the water, eventhough the speed and seperation is greater in the water.

The pebbles are analagous to a mechanical wave, their seperation is analagous to the wavelength.

Answer 3

Because the frequency of the source is exactly the same as the frequency at which the waves hit the boundary, which is therefore the frequency at which the other medium gets excited into "waving." To see this, imagine that one crest hits the boundary at t=0. The next crest has to travel a wavelength and so will hit the boundary one period later. So the period at which the boundary--and hence the other region--is hit is the same as the period of the source. Try this experiment. Tap your tabletop with a certain frequency. Everything on your tabletop will start to bounce or jiggle or whatever with the same frequency. That's the idea.

Now the wavelength corresponding to a frequency of excitation is a property of the medium--how quickly does the next point over respond to a jiggling of the one before it? This depends on how these points are connected together. If thery are stiffly connected then they move rigidly together, and if they are loosely connected one may move a lot before the other notices. Stuff like this determines the wavelength, because the shape of the wave is just the amplitude per unit phase along the direction of motion.

Answer 4

Sound waves travel faster through water than through air and faster along a steel bar than through water (or air). If you tap on an object (with drum sticks?) at 60 beats per minute, that is the frequency of the beats. Although the length of time for each tap to propagate a given distance is different for the different media (1,100 feet per second for air) you can't delay the frequency of the taps at the other end; only the arrival. There will still be 60 taps per minute, right? Using different tuning forks to create different frequencies is not much different than using drum taps; even if the vibrations are imposed on a pipe full of water and audible via the air at the same time.

Answer 5

For an EM wave, each photon has an energy that is proportional to it's frequency (which is Plancks Constant)

Since energy *must* stay the same, the frequency cannot vary, but the wavelength can (and does) as the wave propagates through anything except free space.


Doug

Answer 6

Energy is lost in the transfer in the form of sound, heat etc. Amplitude suffers.

Answer 7

its frequency is its fingerprint