One radio transmitter A operating at 60.0 MHz is 10.0 m from another similar transmitter B that is 180° out of phase with transmitter A. The observer moves n × 10⁻² m from transmitter A toward transmitter B along the line connecting A and B to reach the nearest point where the two beams are in phase. Find n.
Physics · Wave Optics · interferece of light and huygen principle
JEE Mains

Question

One radio transmitter A operating at 60.0 MHz is 10.0 m from another similar transmitter B that is 180° out of phase with transmitter A. The observer moves n × 10⁻² m from transmitter A toward transmitter B along the line connecting A and B to reach the nearest point where the two beams are in phase. Find n.

Physics · Wave Optics · interferece of light and huygen principle

G1 Physics · Accepted Answer

At 60 MHz, λ=c/f=5 m. The sources are π out of phase. For a point x from A, path difference is Δ=10⁻²x. To compensate the initial π phase, Δ=(n+1/2)λ. The nearest x>0 gives Δ=7.5 m, so 10⁻²x=7.5 and x=1.25 m=125×10⁻² m. Answer: 125.