Question

Two out-of-phase radio antennas at X= + 300m on the x-axis are emitting 3.0 MHz radio waves.Is the point (x,y) =(300m, 800m) a point of maximum constructive interference, perfect destructive interference, or something in between?

Answer 1

(300 m, 800 m) (-300 m,0) (300 m, 0) The distance of the point (300 m, 800 m) to first radio station situates at x $1-yl 600 m)' + (800 m)' = 1000 m The distance of the point from the second radio station is, s, = 800 m The path diff erence between the two waves arriving at the given point is, S,-s, = 1000 m-800 m-200 m The wavelength of the waves is, 300 m is, c 3x108 m/s v 3x10 Hz -100 m Condition for constructive interference is, path difference mi Where, m 1,2,3 Path difference is equal to mA s-s2 = mn = (2)(100 m) = 200 m Since, the two waves are initially out of phase, the waves after reaching the given point also are in out of phase Therefore, the given point is a point of destructive interference

Answer 2

The distance between the first speaker bypythagorasR₂ = √ [ (6m)² + (8m)²]= 10 mThe path differrence for constructiveinterference is= R₂ -R₁ = m λ here m= ±1, ±2, ±3 ........destructive intereference is= R₂ -R₁ = [ m + (1/2)]λ m=±1, ±2, ±3 ........soR₂- R₁ == 10 -8 = 2 mif m =1 then λ=2m which signifiesthere is a constructive intererence