Two radio frequency sources broadcast waves of the same frequency. They are placed 1.0 m apart. Let the x-axis be the line from one source to the other, and let x = 0 be at one of the sources.
Nodes are observed at x = 0.24 m, x = 0.49 m, x = 0.74 m.
1) What is the frequency of the two sources?
2) What is the difference between their phase constants?
The Attempt at a Solution
I've simplified the numbers from the original problem to hopefully make things easier. Other than that, the wording is the same.
1) The frequency of the two sources:
I know that the distance d1between two nodes is
d1 = 0.49 m - 0.24 m = 0.25 m .
And the wavelength is twice the distance between nodes.
wavelength = 2d1 = 2(0.25 m) = 0.50 m .
Does this mean that the frequency f is the speed of light divided by wavelength?
f = c/wavelength = 3.00E8 / 0.25 m = 1.2E9 Hz
Not sure if that makes sense...
2) I am really confused about this part.
We can calculate the wave number k,
k = 2pi / wavelength = 2pi / 0.50 m = 4pi rad/m .
And we are given nodes, so we want to use an equation for destructive interference?
(m + 1/2)2pi = k(delta)r + (delta)phi0 = pi when m = 0
But how do I find out what (delta)r is?
A push in the right direction would be appreciated!