What is the Width of the Antenna for Optimizing TV Reception on Channel 10?

[Okazaki]

Homework Statement

The half wavelength "dipole" loop roof television antenna is most sensitive to electromagnetic waves with a wavelength twice the width of the antenna. The frequency of the waves for TV channel 10 is 200 MHz. If you want to optimize the TV reception for channel 10, how wide would you construct this antenna?

Homework Equations

f = v/λ = ω/(2π) = n (v/2L)
v = ω/k = λ/T = λf

The Attempt at a Solution

No matter how hard I try, everything keeps cancelling out. I just can't do this problem!

ω = 2πf
T = 1/f
k = vω
v = 2Lω/(2πn)
= Lω/(πn)

But now, there are just too many unknowns. I don't even know where to begin to substitute. :/ I'm just so frustrated right now. Waves are killing me. I have like, three problems left in this homework assignment, and none of them make sense to me (so I can't skip this one and move on.)

 

[rude man]

What's the wavelength of the 200 MHz signal?
Then it says the antenna width should be half the wavelength of the signal.
What could be simpler?

 

[Okazaki]

What's the wavelength of the 200 MHz signal?
Then it says the antenna width should be half the wavelength of the signal.
What could be simpler?

Oh, λν = c.

Literally, the one formula not in my book.

 

[rude man]

Oh, λν = c.

Literally, the one formula not in my book.

C'mon, has to be!