W9_parallel_resonance.eps

388 Week 11: Light

Moving Receiver

Source Receiver

λ

vr

cT’ v T’r

Figure 154: Wave geometry for Doppler shift of a moving receiver.

If a frequency-sensitive detector of light (such as the eye or a camera) is movingtowards

a fixed source at speedvr, it moves into a wave that is travelling at the speed of light

and “meets the oncoming wavefront half way” (not literally half way)soonerthan it

would have if it were at rest. This shortened periodT′can easily be determined from

the geometry above, whereλ=cT= (c+vr)T′:

cT = (c+vr)T′

T = (1 +vr

c

)T′

1

T′

=^1

T

(1 +vr

c

)

f′ = f(1 +

vr

c

) (955)

As before, if the receiver is moving away, it decreasesf′instead of increasing it, so that

the general rule is:

f′=f(1±

vr

c

) (956)

for a receiver moving towards (+) or away from (-) the source.

Moving Source and Moving Receiver

The rule is just the product of the two rules:

f′=f

(1±vcr)

(1∓vcs) (957)

It is interesting to note that if a source is moving at the speed of light(where these

expressions are no longer valid, alas, although they still capturepartof the shift) the

frequencyf′goes toinfinity. This divergence occurs in the relativistic expression as well,

and is the moral equivalent of asonic boomonly with light.

Although particles cannot go faster than lightin a vacuum, this is actually a physical

possibilityinside a medium. Consider an electron travelling at 0.99c and entering a piece

of glass where the speed of light is only approximately 0.67c. The ”lightboom” given off

by the superluminal particle in the glass isclearly visible(experimentally) and is called

Cerenkov radiation. Cerenkov radiation is the basis of some of the high-energy particle

detectors used in many of the big accelerator laboratories in high energy nuclear physics.