Saved Bookmarks
| 1. |
Distinguish between Cohernt and Incoherent addition of waves. Develop the theory of constructive interference. |
|
Answer» Solution :Coherent sources: The two sources which maintain zero (or) any constant phase relation between themselves are KNOWN as Coherent sources: Incoherent sources: If the phase difference changes with TIME, the two sources are known as incoherent sources. THEORY of constructive and destructive interference: Let the waves of two coherent sources be `y_(1)=a sin omegat.....(1)` `y_(2)=a sin (omegat+phi) .....(2)` where is a amplitude and `phi` is the phase difference between two displacements. According to superposition principle `y=y_(1)+y_(2)` `y=a sin omegat+a sin (omegat+phi)+a sin omegat cos phi+a cos sin phi` `y=a sin omegat[1+cos phi]+cos omegat[a sin phi]....(3)` Let `A cos phi=a(1+cos phi]....(4)` `A sin phi=a sin phi ....(5)` Substituting equations (4) and (5) in equation (3) `y=A sin omegat, cos phi+A cos omegat sin THETA` `y=A sin (omegat+phi).....(6)` Where A is reulstant amplitude. Squaring equations (4) and (5). Then adding `A^(2)[cos^(2)phi+sin^(2)phi]=a^(2)[1+cos^(2)phi+2cos phi+sin^(2)phi]` `A^(2)[1]=a^(2)[1+1+2 +cos phi]""(therefore I=A^(2))` `I=2a^2 xx 2cos^(2) ""(phi)/(2)` `I=4a^(2) cos^(2) ""(phi)/(2)` `I=4I_(0)cos^(2)""(phi)/(2)......(7)""(therefore I_(0)=a^(2))` Case (i) For constructive interference: Intensity should be MAXIMUM. `cos ""(phi)/(2)=1 Rightarrow phi=2npi` Where `n=0,1,2,3,......Rightarrow phi=0, 2pi, 4pi,6x ......I_("max")=4I_(0)` Case (ii) For destructive interference: Intensity should be minimum i.e, `cos phi=0 Rightarrow phi =(2n+1)pi, " where n "=0,1,2,3,......,phi=pi,3pi,5pi Rightarrow I_(min)=0` 
|
|