Question

In this problem wa wil consider the path differencs between two waves emitted by two source constractive interfenence to occur the net phase diference between that start out in phase. Recall that for rvo waves must be 0, 2r 4.., and for destructive interference to occur the net phase difference betweern two waves must be 3 5 ! Iwo source are in phase and emit waves that have a wavelength of 0.44 m. Determine whether constructive, occurs at a point whose distances form the two sources are as follows: length diflerence between the waves and relate this mumber to the wavelengih.) or destructive interference o (Hint: Find the path l (a) 1.32 and 3.08 meters (b) 2.67 and 3.33 meters (c) 2.20 and 3.74 meters (d) 1.10 and 4.18 meters

Answer 1

For two waves to interfere Construchvely, Ane phase di#erence should be of he order 2ne o, 2T, 47,So diflevence and tor destuctve imterferenc the phasederece shoue be of the order (en +) i-e T, 3π, 5f-... etc. so herethe path difference would be-, 3a, etc. . So the path d//evence should be at the order λ,2>, y desthuchve in er ence inter Given that two waves o혹 wave/eneh as 0-44 m are inter tevind at apoint. (a) dl=/.32 m, d2-3,08 m . So the path difference is δd-4-a, = 1.16 m , sd 4λ , which implies that -the 1.76 m . and 4λ_ 4x o 44 interference is Cnstuch ve (a) di 2.67 m, d 3.33 m. Here path difference is Sd d-d . 6 and 3A-3(0-46) -0.66 m, -ל Ed SA- , implies Dest achve interference. (C) d'= 2.2 m, d2= 3.74 m. Pa Sd-d2-d1= 1.54 m 2- 2 th difference is and 7A- 7(0-44) = 1.54 m , → Sd- TA , imptes Destuchve interference estrucive interference 2 4.18 m, Path diffvence is sd - d, -d, - 3.08 m (d) d 1-10 m, d Construchve inter terence and てλ=て(0.44) = 3,08 m, ヲ sd =てa, impf;es