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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Length contraction and wave length transformation

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**