The definition of wavelength is different

[qwwq]

Ok, this is bugging the hell out of me. Wikipedia says the definition of wavelength is "the distance over which the wave's shape repeats", as I always have known to be. Here is the pic :

https://en.wikipedia.org/wiki/File:Sine_wavelength.svg

But in my book, "Engineering Electromagnetics" by W.H.Hayt and J.A.Buck, under the chapter of transmission lines, it is said that the same is \[\lambda\]/2, and not \[\lambda\]. I have also referred to other books on transmission lines, they all state the same. Many of the sums given in the texts and also those that comes in exams also requires to use this definition. Definitely there is something conceptual here, which I am missing. I have attached the scan of that particular page from the book. Please help. Looking forward to your response.

Regards.

 

[SpaceDust]

In transmission lines, the wave repeats at half of lambda as the second half or the negative have also appears on positive axis, like the plot it a full wave rectifier. This is due to the standing waves that are formed in a transmission line, so for one min to min or max to max of wave, it is lambda/2 but not lambda, the wiki's definition is also right but more of for waves in free space or were you have both positive and negative cycles. Hayt is a good book, go thru the theory in it for more clarifications..!!

 

[qwwq]

Thank you for your reply. Agreed, that the entire wave representing the voltage lies in the positive zone, with the maxima being (1+|Γ|)*Vo and the minima being at (1-|Γ|)*Vo. But I can't see how the shape is like that of a full wave rectified waveform, or something like |sin(x)|+k. According to the diagram given in the scan (which I have attached earlier), the voltage waveform is clearly like a normal single frequency sine wave. And hence the spatial distance between two successive maxima and minima seems to be λ, whereas I the diagram itself it is mentioned that the distance is λ/2.

 

[biff44]

wavelength in a transmission line is the same, just lengthened a little due to dielectric constant.

You are confusing wavelength along the line, with reflection coefficiend. To see a reflection, then energy travels down, and then back again. So lambda/2 in one direction become lambda round trip

 

[qwwq]

Sir, appreciate your response. Could you be more specific how we can relate the wave length of a transmission line with dielectric constant of the material separating the two conducting wires of a transmission line? And V(x) = Vo*(1+Γ(x)) is the waveform that's supposed to incorporate the effects of the incident wave from the generator, it's reflection from the load and then it's further reflection from the generator back to the load and so on. So, λ, being the wavelength of this wave should have been the distance at which the wave repeats. But it is double of that, making the crest to crest distance half of the "claimed" λ. If anybody could give a more mathematical reason, that would be more profound.

 

[qwwq]

Please post some solutions