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[SOLVED] Interference of waves - 2 point source Question
Two towers of a radio station are 400 m apart along an east-west line. The towers act essentially as point sources, radiating in phase at a frequency of 1.00 x 10^6 Hz.
a) In what directions is the intensity of the radio signal at a maximum for listeners 20 km north of the transmitter (but not necessarily directly north of it)?
b) In which directions would you find the intensity at a minimum, north of the transmitter, if the towers were to start transmitting in opposite phase?
(n-1/2)lamda = sin theta
d
where n - the number of nodes
theta - the angle between nodes
d - distance between 2 point sources
velocity= lamda x frequency
I thought that I want to figure out the angle between the central max, and the first node - where the radio signal would be at a minimum (due to destructive interference) and then divide it by 2 to get the angle at the maximum (constructive interference).
lamda= 3.00 x 10^8 m/s = 300 m
1.00 x 10 ^ 6 Hz
( 300m) (1-1/2)= sin theta
400 m
theta = 22 degrees / 2
= 11 degrees
My answer was N 11 E or N 11 W, whereas the real answer should be N 49 E or N 49 W.
Help please!
Thanks!
Homework Statement
Two towers of a radio station are 400 m apart along an east-west line. The towers act essentially as point sources, radiating in phase at a frequency of 1.00 x 10^6 Hz.
a) In what directions is the intensity of the radio signal at a maximum for listeners 20 km north of the transmitter (but not necessarily directly north of it)?
b) In which directions would you find the intensity at a minimum, north of the transmitter, if the towers were to start transmitting in opposite phase?
Homework Equations
(n-1/2)lamda = sin theta
d
where n - the number of nodes
theta - the angle between nodes
d - distance between 2 point sources
velocity= lamda x frequency
The Attempt at a Solution
I thought that I want to figure out the angle between the central max, and the first node - where the radio signal would be at a minimum (due to destructive interference) and then divide it by 2 to get the angle at the maximum (constructive interference).
lamda= 3.00 x 10^8 m/s = 300 m
1.00 x 10 ^ 6 Hz
( 300m) (1-1/2)= sin theta
400 m
theta = 22 degrees / 2
= 11 degrees
My answer was N 11 E or N 11 W, whereas the real answer should be N 49 E or N 49 W.
Help please!
Thanks!
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