A radio station operating at 102.9 MHz broadcasts from two identical antennae at
ID: 1500121 • Letter: A
Question
A radio station operating at 102.9 MHz broadcasts from two identical antennae at the same elevation but separated by a 9.24-m horizontal distance (labeled d in the diagram). A maximum signal is found along the midline, perpendicular to d at its midpoint and extending horizontally in both directions. If the midline is taken as 0 deg.
A.) If the midline is taken at 0 deg, what is the smallest angle theta where a maximum signal is detected?
B.) What is the second smallest angle theta where a maximum signal is detected?
C.) What is the smallest angle where a minimum signal can be detected?
D.) What is the second smallest angle where a minimum signal can be detected?
Explanation / Answer
f=102.9 Mhz = 102.9 * 106 Hz
c= speed of light = 3*108 m/s
wavelength = = c/f = 3*108 m/s / 102.9 * 106 =2.915 m
we know that where a maximum signal is detected , constructive interference occurs.
and for constructive interefernce
a sin = m
m=0,1,2,...
where a = source seperation = 9.24 m
hence 1 = 2.915 m / 9.24 m = 0.315 rad = 18.3 degree
For 2nd maxima
a sin = 2
hence 2 = 39.12 degree
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minimum signal can be detected where destructive interference occurs.
and conditon for destructive interference:-
a sin = (m-1/2)
where m = 1,2,3,....
hence for minimum signal 1=9.07 degree
for 2nd minima
a sin2=(2-1/2) = 1.5
2 = 28.24 degree