A radio station operating at 102.9 MHz broadcasts from two identical antennae at

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

---------------------------------------------------------------------------------------

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.