Research website of Vyacheslav Gorchilin
2017-09-28
The transformation of transverse waves into longitudinal
This application will need to obtain the longitudinal magnetic component from standing waves, and for a General understanding of longitudinal waves, as a class. Here we show how to obtain the longitudinal wave from the sum of the stand-up and derive the necessary condition.
For starters, potreniruemsya in the online calculator to obtain standing waves with different frequency. Left, top to bottom are the time scale and amplitude — what the user sees on the oscilloscope. From left to right is our resonator at half wave length L/2. The wave frequency will determine the multiples of the fundamental harmonics: 2nd, 3rd, 4th and 5th. The first harmonic, by definition, this is the basic or reference frequency. It will start and get the simplest standing wave — half-wave (Fig. 1).
Fig.1. Wave at half the length

Despite the image on the page you can generate this wave in the online calculator. Because it modeled real-world process, then you need to wait a bit until the transition process and established a fixed pattern. Normally, it takes less than a minute.

Next, we will move to get the result and because we imagine a wave with the already necessary amplitude. The second wave will full-wave (Fig. 2). In other words, now in the same length of the resonator fit in twice the half-wave, since it specifies the frequency increased twice.
Fig.2. Wave in full length
The same principle will receive the waves at three second (Fig. 3), four second (Fig. 4) and five second length (Fig. 5).
Fig.3. Wave three second length
Fig.4. Wave four of the second length
Fig.5. Wave five the second length
And now let's sum up together all previously obtained wave. The result (Fig. 6) needs to surprise many! It would seem that we received a traveling wave, but it is not the sum of standing waves will also be standing wave. In fact, so we have received from the shear wave is longitudinal, but the same standing as if to take each of its components separately. By the way, this dispels the myth that standing waves do not transfer energy :) In support of this, we suggest looking at the experience of Professor E. Laithwaite [1] and experiment [2].
Fig.6. The sum of all waves
A necessary and sufficient condition
The following conclusion from the foregoing it may be a necessary and sufficient condition for the conversion of transverse waves into longitudinal ones. Try to remove from the received result all even harmonics — lookwhat happened. As you can see, the longitudinal component disappeared! Strictly mathematically it is displayed here, and while we important qualitative result:

longitudinal wave from the amount standing cross can be obtained only if in this set, along with odd, will attend at least one wave with even harmonics.

Dear readers, you can practice with different proportions of the resonator, such as a quarter wave (L/4), but the best results will give a half-wave, which should be used in real devices.
Materials used
1. Professor Eric Laithwaite: Magnetic River. 1975
2. YouTube. Tubo de Rubens. 2023