Why is Half a Wavelength the First Harmonic in Standing Wave Harmonics?

[elliottmarter]

Why does half a wave length and not a full wave length constitute the first harmonic?



v=$$\lambda$$f



because a standing waves can be made with two half waves traveling in opposite directions?

 

[jdwood983]

Here is a good resource on http://www.physicsclassroom.com/Class/waves/U10L4e.cfm" .

Basically you are right, but your terminology isn't quite correct. The wavelength is the length up and back the string, so $\lambda=2L\rightarrow L=\frac{1}{2}\lambda$.

 

[elliottmarter]

Thanks a lot, that helped