The factor γ in the Doppler formula (15.64), which can be ascribed to time dilation, means that even when θ = 90° there is a Doppler shift. (In classical physics there is no Doppler shift when θ = 90° and the source has zero velocity in the direction of the observer.) This transverse Doppler shift is therefore a test of time dilation, and has yielded some very accurate tests of the theory. However, except when the source is moving very close to the speed of light, the transverse shift is quite small.
(a) If V = 0.2c, what is the percentage shift when θ = 90°?
(b) Compare this with the shift when the source approaches the observer head-on.