18 The Doppler Effect
205
Fig. 18.4 Experimental construction for the transversal Doppler effect. The observer O rests in
the medium. The emitter S moves with a velocity v perpendicular to the direction of the waves the
emitter sends out
Fig. 18.5 The assumptions for observing the transversal Doppler effect: The distance v/ν o covered
by the emitter between sending out two-wave crests has to be much smaller than the shortest
perpendicular distance R o between emitter and observer
Therefore our condition L R o simply means
v
2
2R o ν 2
o
R o , thus
v
2
c
2
T
λ
2
o
2R o
R o .
We therefore find the equation v/c T R o
√
2/λ o for the condition ‘large distance’, or simply
v
c T
R o
λ o
.
(232)
In the limit of an ‘infinitely far away’ emitter, this condition would always be
fulfilled.
205
Fig. 18.4 Experimental construction for the transversal Doppler effect. The observer O rests in
the medium. The emitter S moves with a velocity v perpendicular to the direction of the waves the
emitter sends out
Fig. 18.5 The assumptions for observing the transversal Doppler effect: The distance v/ν o covered
by the emitter between sending out two-wave crests has to be much smaller than the shortest
perpendicular distance R o between emitter and observer
Therefore our condition L R o simply means
v
2
2R o ν 2
o
R o , thus
v
2
c
2
T
λ
2
o
2R o
R o .
We therefore find the equation v/c T R o
√
2/λ o for the condition ‘large distance’, or simply
v
c T
R o
λ o
.
(232)
In the limit of an ‘infinitely far away’ emitter, this condition would always be
fulfilled.