Interference of waves - 2 point source Question

[anachronautic]

[SOLVED] Interference of waves - 2 point source Question

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!

 

[alphysicist]

Hi anachronautic,

You did find the first minimum; however, there is no maximum between that and the central maximum. Starting at the center and going out, you have :

central maximum (at zero degrees), 1st minimum, 1st maximum, 2nd minimum,...

But you can find the first maximum directly from the constructive condition:

$$d \sin\theta= m \lambda$$

 

[anachronautic]

Thanks alphysicist!
It all makes sense now! :)