consider a rod of proper length Lo located along the overlapped OX(O'X') axes of the I and I' inertial reference frames in the standard arrangement I' moving relative to I' with speed V. The rod moves with speed U relative to I and with speed U' relative to I'. The measured length of the rod is(adsbygoogle = window.adsbygoogle || []).push({});

L=g(U)Lo (1)

L'=g(U')Lo (2)

in I and in I' respectively. Eliminating Lo between (1) and (2) we obtain

L=L'g(U)/g(U'). (3)

Expressing the right side of (3) as a function of U' only, via the addition law of relativistic velocities we obtain

L=L'g(V)/1+u'V/cc (4)

an equation that relates two non-proper lengths.

Is it correct to consider that the derivation presented above represents a derivtion for the relationship betwee the wavelengths of the same acoustic (mechanical) wave that propagates with speeds U and U' relative to I and I' respectively?

Did you find that derivation somewhere in the literature of the subject?

Thanks.

sine ira et studio

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# Length contraction and wave length transformation

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