How Do Radio Frequency Sources Create Interference Patterns?

[nietzsche]

Homework Statement

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!

 

[ehild]

The first wave starts from x=0 with a phase constant phi and travels in the +x direction. The other wave starts at x=1 m, with zero phase constant and travels in the - x direction. What will be the phase of both waves at one of the nodes?

ehild