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What is the relationship between "the second resonance " and string and the wavelength. Like in this question: if the length of the string is 2cm with second resonance, then what is wavelength?

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You know about (speed)=(wavelength)*(frequency) and that the wave speed is constant if the tension is constant. –  ja72 May 13 '13 at 19:06
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1 Answer

The first resonant vibrational mode for a string clamped at both ends looks like:

fundamental harmonic

You should be able to deduce the wavelength from that diagram. The second mode looks like:

second harmonic

Both of the images above are from http://www.clickandlearn.org/Physics/sph3u/Music/Music.htm and that site will spell it out in more detail for you.

If your string length is $2\:\mathrm{cm}$ then the wavelength of the first vibrational harmonic is $4\:\mathrm{cm}$. The second vibrational mode has a wavelength of $2\:\mathrm{cm}$.

If the string is open at one or both ends the modes are different however using the link above you should be able to figure it out without issue.

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