Physics of The Very Smal S2, 2015 Problem Solving Task 4 Optics Exercise 35.3: E

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Physics of The Very Smal S2, 2015 Problem Solving Task 4 Optics Exercise 35.3: Engineering Exercise 35.3: Engineering A radio transmitting station operating at a frequency of 125 MHz as two identical antennas that radiate in phase. Antenna Bis 8.95 m to the right of antenna A. Consider point P between the antennas and along the line connecting them, a horizontal distance r to the right of antenna A. session masteringphysics.com Part A For what values of a will constructive interference occur at point P? Enter your answers in ascending order separated by a comma AEG Submit My Answers Give Up Signed in as n9375104 ALKHALDY Help Close Resources previous l 4 of 10 I next Provide Feedback Continue

Explanation / Answer

for constructive interference, the path difference should be integer multiple of wavelength.

here speed of the wave=3*10^8 m/s

frequency=125*10^6 Hz

then wavelength=speed of the wave/frequency of the wave=2.4 m

distance of point P from A=x

then distance of point P from B=8.95-x

then path difference=8.95-x-x=8.95-2*x

so for constructive interference,

8.95-2*x=n*2.4

where n=0,1,-1,2,-2,...etc

n=0

==>2*x=8.95
==>x=8.95/2=4.475 m

for n=1:

8.95-2*x=2.4

==>x=(8.95-2.4)/2=3.275 m

for n=-1:

8.95-2*x=-2.4

==>x=(8.95+2.4)/2=5.675 m

for n=2:

8.95-2*x=2*2.4

==>x=(8.95-2*2.4)/2=2.075 m

for n=-2:

8.95-2*x=-2*2.4

==>x=6.875 m

for n=3:

8.95-2*x=3*2.4

==>x=0.875 m

for n=-3 m:

8.95-2*x=-3*2.4

==>x=8.075 m

for n=4, there is no positive solution for x.

hence answers are:

0.875 m, 2.075 m, 3.275 m, 4.475 m, 5.675 m, 6.875 m. 8.075 m

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