Transmission Lines & Impedance Matching

[AngelofMusic]

Hi all, I'm currently studying up on transmission lines for my next midterm, and I stumble onto this problem.
Given information: A 800 MHz transmission line that is lossless
- Vmax, Vmin, V_L for a given load impedance R_L.
- Characteristic impedance of a line
- length of a line & \lambda
Is it possible to find the amplitude of the voltage (Vmatched) assuming that instead of the original load impedance, the line is now matched?
So far, I've tried to use the voltage equation of a transmission line
V(z) = \frac{Z_0 V_g}{Z_0 + Z_g} e^{-j\beta z} [1+\gamma e^{-j2\beta (l-z)}]
I set V(z=l) = V_L, which is given. And I solve for the value of the big fraction in front. Then I use that equation again, except set \gamma = 0 for the matched case.
Is this the right approach to solving this problem?
I do get an answer out of this one, but it's not one that seems obvious or intuitive. Is there a better approach to this? Or an incredibly simple answer to this problem?
Any help would be appreciated!

 

[WalterContrata]

Standing Wave

Perhaps I am wrong, but I think there is a simple way.
Are Vmax and Vmin given? They result from adding or subtracting a wave going towards the load and a reflected wave from the load. Can you solve for the amplitudes of those two waves?
If the load were macthed, what is the amplitude of the incoming wave? The reflected wave?
Hope this helps.