According to the valence bond theory the triple bond in ethyne consists of

            According to the valence bond theory the triple bond in ethyne consists of one sigma bond and two pi bonds.

Explanation:
                   Atomic number of carbon is 6. The ground state electronic configuration of carbon is as follow,

                                         1s², 2s², 2p²

And the excited state electronic configuration of carbon is as follow,

                                         1s², 2s¹, 2px¹, 2py¹, 2pz¹

In ethyne the 2s¹ orbital and 2px¹ orbitals having unpaired electrons form sigma bonds by head to head overlapping with orbitals of hydrogen atom and carbon atom. The remaining 2py¹ and 2pz¹ orbitals of both carbons overlap perpendicular to the existing sigma bond resulting in the formation of two pi bonds.

Because a model would make the investigation easier to understand