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
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
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 :)
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 one. Try to remove from the received result all even harmonics — look
what happened. As you can see, the longitudinal component disappeared! Strictly mathematically it is displayed here
, and while we important qualitative result:
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.