- #1
etotheipi
If the source is at ##(t,0)## in ##S## and the receiver is at ##(t',0)## in ##S'## which moves at ##\beta_x## w.r.t. ##S##, then by considering two crests at ##(0,0)## and ##(T_s, 0)## in the source frame ##S## and transforming these events into ##S'## we can derive that ##\lambda_{r} = \lambda_{s} \sqrt{\frac{1+\beta_x}{1-\beta_x}}##.
That's the formula that I see everywhere, and it seems okay if the origin of ##S'## is in the region ##x>0##, but if the origin of ##S'## is in the region ##x<0## then wouldn't we have ##\lambda_{r} = \lambda_{s} \sqrt{\frac{1-\beta_x}{1+\beta_x}}##, because of the left-right symmetry?
I've never seen this mentioned anywhere, so I wondered if someone could clarify? Thanks
That's the formula that I see everywhere, and it seems okay if the origin of ##S'## is in the region ##x>0##, but if the origin of ##S'## is in the region ##x<0## then wouldn't we have ##\lambda_{r} = \lambda_{s} \sqrt{\frac{1-\beta_x}{1+\beta_x}}##, because of the left-right symmetry?
I've never seen this mentioned anywhere, so I wondered if someone could clarify? Thanks
Last edited by a moderator: