(a) Show that Eq. (16.30) can be written as (b) Use the
Chapter 16, Problem 16.78(choose chapter or problem)
(a) Show that Eq. (16.30) can be written as
\(f_{\mathrm{R}}=f_{\mathrm{S}}\left(1-\frac{v}{c}\right)^{1 / 2}\left(1+\frac{v}{c}\right)^{-1 / 2}\)
(b) Use the binomial theorem to show that if \(v\ \ll\ c\) this is approximately equal to
\(f_{\mathrm{R}}=f_{\mathrm{S}}\left(1-\frac{v}{c}\right)\)
(c) A pilotless reconnaissance aircraft emits a radio signal with a frequency of 243 MHz. It is flying directly toward a test engineer on the ground. The engineer detects beats between the received signal and a local signal also of frequency 243 MHz. The beat frequency is 46.0 Hz. What is the speed of the aircraft? (Radio waves travel at the speed of light, \(c=3.00\times10^8\mathrm{\ m}/\mathrm{s}\).)
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