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I can't get my head round this:

Suppose I have two transmitters A and B, at different distances (d_A, d_B) from a reciever, C.

Each transmitter transmits a sinusoidal wave towards the receiver, which I will be modelling as 1 dimensional travelling waves, each given by the equation:

y(x,t) = Asin(wt - kx + θ).

The idea is that so long as the transmission wavelength used is twice the distance from C to MAX{d_A,d_B}, a phase comparator can detect the difference in phase between the two signals, due to changes in their relative distances from the receiver C (Since one will travel a fraction of a wvelength further than the other).

This is where I'm stuck:

Now suppose B is further than A, so that d_B > d_a, and that both transmitted waves have exactly the same frequency, and starting phase (Meaning if t_A and t_B are the times each transmitter starts its tranmission, then for a given value of x, y_A = y_B - i.e. they are spatially coherent - I think that is the right term?). I'm also assuming that the amplitude of both waves at the receiver is 1, to simplify the scenario.

What I want to know is that if there is a difference between the transmission times, t_A and t_B, of the two transmitters, will it cause a difference in the measured phase at the reciever (Hence affecting the reliability of the distance measurement based on the phase difference)?

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# Travelling wave phase difference problem

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