25 (a) Let frame O move with speed v in the x-direction relative to O. Let a photon have frequency v in O and move at an angle 0 with respect to O's x axis. Show that its frequency in Õ is D/v = (1 – v cos 0)//(1 – v²). (2.42) (b) Even when the motion of the photon is perpendicular to the x axis (0 = 1/2) there is a frequency shift. This is called the transverse Doppler shift, and arises because of the time dilation. At what angle 0 does the photon have to move so that there is no Doppler shift between O and Õ? (c) Use Eqs. (2.35) and (2.38) to calculate Eq. (2.42). %3D - p- Ūobs = Ē. (2.35) E = hv, (2.38)
25 (a) Let frame O move with speed v in the x-direction relative to O. Let a photon have frequency v in O and move at an angle 0 with respect to O's x axis. Show that its frequency in Õ is D/v = (1 – v cos 0)//(1 – v²). (2.42) (b) Even when the motion of the photon is perpendicular to the x axis (0 = 1/2) there is a frequency shift. This is called the transverse Doppler shift, and arises because of the time dilation. At what angle 0 does the photon have to move so that there is no Doppler shift between O and Õ? (c) Use Eqs. (2.35) and (2.38) to calculate Eq. (2.42). %3D - p- Ūobs = Ē. (2.35) E = hv, (2.38)
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Transcribed Image Text:25 (a) Let frame O move with speed v in the x-direction relative to O. Let a photon have
frequency v in O and move at an angle 0 with respect to O's x axis. Show that its
frequency in Ō is
D/v = (1 – v cos 0)/ /(1 – v²).
(2.42)
(b) Even when the motion of the photon is perpendicular to the x axis (0 = 1/2) there
is a frequency shift. This is called the transverse Doppler shift, and arises because
of the time dilation. At what angle 0 does the photon have to move so that there is
no Doppler shift between O and Õ?
(c) Use Eqs. (2.35) and (2.38) to calculate Eq. (2.42).
- p. Ūobs = Ē.
(2.35)
E = hv,
(2.38)
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