For constructive I can understand. But destructive I can't.
I can not picture the shape of two pulses or waves maybe that form the resulting standing wave. The places where waves are canceled just look so perfect and so like a normal wave.
[Physics] How are standing waves a result of constructive and destructive interferences
interferencesuperpositionwaves
Related Solutions
The basic surprise here is that energy is always conserved when waves superimpose. This seems like it shouldn't be true, since superposition causes amplitudes to add, whereas energy is proportional to the square of the amplitude. This nonlinear relationship makes it seem like energy should not be additive, and therefore can't be conserved.
This is a generic issue for waves, not just light waves, so let's consider it first in the case of waves on a string.
For example, if you take a light string and a heavy string and join them together end to end, waves that hit the boundary will be partially reflected and partially transmitted. One thing we can predict immediately is that energy is conserved, since the interaction between neighboring bits of the strings are governed by the ordinary laws of mechanics. Since energy is conserved at all points in space and time during the evolution of the waves, it must be conserved over all.
Another helpful example is a single uniform string, with oppositely propagating sine waves of the same wavelength encountering one another and superposing. There are moments when the waves cancel and the string is flat, but the motion recovers after such a moment -- was energy destroyed and then created again? No, because the flatness of the string only implied zero potential energy. The string had kinetic energy at the moment of flatness. If each wave separately had 1 unit of KE and 1 unit of PE, for a total of 4 units, then at the moment of flatness, we have 4 units of KE (due to doubled velocity) and 0 units of PE.
So in general, the idea is that conservation of energy has to be proved from the equations of motion, which are a differential equation holding at every point in space and time. For light, these equations of motion are Maxwell's equations, and one can indeed prove conservation of energy from them.
It's a nice exercise to verify conservation of energy for the case of oppositely propagating light waves, as in the second example with the rope above.
I can set up a thin film such that the reflectance is zero (R = 0) and transmittance is one (T = 1), don’t I need energy in the waves to cause destructive interference to begin with?
(I corrected T = 0 to T = 1 in this quote.)
Here we can analyze the reflected wave as a superposition of waves reflected from the front and back surfaces. Amplitudes add, not energies. Therefore these two waves, each of which individually would have had, say, 1 unit of energy, together do not have to have 1+1=2 units of energy. Their amplitudes add to 0, so together they have 0 units of energy.
The electric and magnetic parts of an electromagnetic wave have the same wavelength and the same spatial relationship, so if the electric parts line up the magnetic ones do, too. There is only one wave, not three. If they are traveling in the same direction (as in a laser) they will stay in phase. Constructive interference works fine-that is what makes lasers work and interference patterns in light.
Best Answer
Take a look at this Desmos animation. Either animate it by clicking the play button next ot the time (t) variable, or drag the slider around to watch the behavior of the waves.
Watch carefully what the standing wave (the black trace) looks like when the waves constructively interfere (I.E. at times when they both look identical) and when the waves destructively interfere (I.E. at times when they looked like mirror images of each other flipped over the y-axis). As you can see, the standing wave is simply the addition of the two traveling waves.