(Mechanical waves) Describe Constructive and Destructive interference using the priciple of superposition.?

Question

Include the significance of this phenomenon in relationship to diffraction.

oops, it is supposed to be "the principle of superposition".

Answer 1

One of the cool physics principles is that waves consist of a fundamental frequency and a whole bunch of constituent frequencies called harmonics. A guy named Fourier found a way to show this by a math technique called (what else) the Fourier expansion. In math talk, we can write F(f) = F(0) + F(f) + F(2f) + ... + F(mf); where F(0) is the fundamental frequency (say middle C on the piano for example and all the F(mf) are the harmonic frequencies.

Well, learned people looked at this and said "Hey this looks like all these other frequencies are superimposed or added on top the fundamental frequency." And, thus, we have the principle of superposition, which simply means all those harmonic frequencies are imposed or added on top of the fundamental frequency.

Turns out (don't you just love that phrase), all waves can be written as a fundamental and superimposed subfrequencies (the harmonics). It also turns out that these harmonics are discrete harmonics...that is, you can't have any frequencies in between them. Each harmonic is an integer (m) multiple of the fundamental freq (f). As a consequence, all harmonics are higher than the fundamental frequency, which is the lowest of all the superposed frequencies. Sometimes F(0) is called the base frequency.

OK then...back to constructive and destructive interference. Constructive simply means two or more frequencies build up (construct) the fundamental frequencies and their harmonics. For example, if we have A(f) = A cos(f) and B(f) = B cos(f); where f = the frequency A(f) + B(f) = (A + B) cos(f) and, by superposition we construct a wave with amplitude (A + B) operating at the same frequency (and its harmonics). When two waves are operating at the same frequency so that they construct, we say they are "in phase" or synced.

A famous example of this is that bridge (I think in Michigan) that self-destructed due to constructive inteference. The winds set the bridge to vibrating at a frequency that was in sync with the natural frequency of the bridge's framework. The amplitudes of the wind and the frame (e.g., A and B) waves started to add up until the stresses tore the bridge apart. So it was constructive interference that caused the destruction...ironic, heh?

Destructive simply means the opposite of constructive, we are subtracting two wave effects. For example, assume A(f) = A cos(f) and B(f) = B sin(f); so that A(f) + B(f) = A cos(f) + B sin(f) = 0 if A = B because the cosine wave in sync with the sine wave cancel (destruct) each other. And remember, we can do these additions and subtractions because of the principle of superposition, which applies to all waves.

Answer 2

properly, i think of of what the persecuted Christians conflict through in different international places the place there is not any non secular freedom. they are consistently conscious that the depraved ruler-deliver of the country will intervene with something God is doing of their lives. An occasion of unfavorable interference could be somebody reporting to the government that somebody is analyzing the Bible. In North Korea this is sufficient to get somebody arrested even however they try this interior the privateness of their own properties. in fact, the teachers attempt to get the infants to record on their mothers and fathers and the government attempt to get all and sundry to record on everybody who has any warning signs of non secular interest that's no longer what the state believes in. that's the worst style of unfavorable interference. advantageous interference could be whilst somebody interferes with the plans of the depraved to interrupt Christianity in any way, shape or style. I somewhat have been acquainted with those style of issues for some years now.