Maximizing and Minimizing Wavelength Contributions in Radiowave Reflection

[Const@ntine]

Homework Statement

The transmitter is on the left, and the receiver is on the right. The transmitter transmits radiowaves. The distance between them is d = 50.0 m & each one's height is h = 35.0 m. The receiver can receive the radiowaves directly from the transmitter, or through reflection by the ground. When the radiowaves hit the ground, there is a phase difference of 180 degrees.

Find which are the maximum wavelength that contribute:

a) Strengthening.
b) Weakening.

Homework Equations

The Attempt at a Solution

I'll be honest here, I've been staring at this for a while and I just don't know where to start. It's probably something simple, but for the life of me I don't know what to do. It's in my Optics Part of the book, Chapter with Thin-Films and contribution by two openings on a board and all that. I'd really appreciate a nude or "directions" on what to look for or something.

Any help is appreciated!

 

[BvU]

If a reflected wave arrives with the same phase, it strengthens the direct ray. Is that a useful hint for you ?

 

[haruspex]

Find which are the maximum wavelength that contribute:

I am not at all sure what this question is asking. Never mind, let's just analyse the set-up and see where it leads.
Suppose the wavelength used is λ. When the wave has traveled distance s, what is the phase difference between the point the wave has reached and the present state at the transmitter? In the diagram, what phase difference will there be between the wave that takes the direct path and the wave that reflect from the ground?

I'd really appreciate a nude

You will need a different forum for that.

 

[Const@ntine]

If a reflected wave arrives with the same phase, it strengthens the direct ray. Is that a useful hint for you ?

Sure, but I'm mostly lost on the "what do I even do here" part. I know what "happens" based on logic, but I'm not sure what I'm looking for, or how to find it.

I am not at all sure what this question is asking.

Well, it's a direct translation, so I'm not sure myself. Best I can come up with is "find the wavelengths with the biggest numerical value that result in either a strengthening or cancelling confluence".

Never mind, let's just analyse the set-up and see where it leads.
Suppose the wavelength used is λ. When the wave has traveled distance s, what is the phase difference between the point the wave has reached and the present state at the transmitter? In the diagram, what phase difference will there be between the wave that takes the direct path and the wave that reflect from the ground?

So I should treat this as a "double slit" problem? Like this:

You will need a different forum for that.

Darn it, I meant to write nudge (keyboard's a tad busted).

 

[CWatters]

So I should treat this as a "double slit" problem? Like this:

Yes. Not exactly the same but the same ideas (eg path lengths differ by multiple of the wave length).

 

[Const@ntine]

So, uh, anybody have any more hints on this? I'm blanking out. I tried treating it as a double slit, with one slit being the "head" of the transmitter and the other being the place where the wavelength reflects, but it didn't work.

 

[ehild]

So, uh, anybody have any more hints on this? I'm blanking out. I tried treating it as a double slit, with one slit being the "head" of the transmitter and the other being the place where the wavelength reflects, but it didn't work.

In both cases, double slit and the direct ray and the reflected one in this problem, the key word is phase difference between the rays which meet. It comes from the path difference and the phase change at reflection. If it is integer multiple of 2π, the rays add up to maximum intensity. If the phase difference is odd number times π, minimum intensity is obtained.

 

[haruspex]

So, uh, anybody have any more hints on this? I'm blanking out. I tried treating it as a double slit, with one slit being the "head" of the transmitter and the other being the place where the wavelength reflects, but it didn't work.

Did you try to answer my questions in post #3?

 

[Const@ntine]

Did you try to answer my questions in post #3?

Yeah, I assumed it was a nudge to get me to look at it as a double-slit problem. Find the angle the two "paths" create and construct the phase-difference from that.

 

[haruspex]

Yeah, I assumed it was a nudge to get me to look at it as a double-slit problem. Find the angle the two "paths" create and construct the phase-difference from that.

So post expressions for the two path lengths.

 

[Const@ntine]

So post expressions for the two path lengths.

I'm a tad stuck on that. If I look for an angleat the starting point, aren't I omitting part of the path of the second radiowave?

 

[haruspex]

I'm a tad stuck on that. If I look for an angleat the starting point, aren't I omitting part of the path of the second radiowave?

What angle?
It is a simple matter of geometry. In the diagram, how far is it along the straight line between the tops of the two towers?
How far is it along the other route? Then add half a wavelength for the second case for the reflection phase shift.
What is then difference between the two path lengths?