Solution Found!
Solved: (a)Show that Eq. (16.30) can be written as Use the
Chapter 16, Problem 78P(choose chapter or problem)
(a) Show that Eq. (16.30) can be written as
\(f_{R}=f_{S}\left(1-\frac{v}{c}\right)^{1 / 2}\left(1+\frac{v}{c}\right)^{-1 / 2}\)
(b) Use the binomial theorem to show that if \(v \ll c\), this is approximately equal to
\(f_{R}=f_{S}\left(1-\frac{v}{c}\right)\)
(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, \(c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\).
Equation Transcription:
Text Transcription:
fR=fs(1-v/c)^½(1+v/c)^-½
v<<c
fR=fs(1-v/c)
c=3.00x10^8 m/s
Questions & Answers
QUESTION:
(a) Show that Eq. (16.30) can be written as
\(f_{R}=f_{S}\left(1-\frac{v}{c}\right)^{1 / 2}\left(1+\frac{v}{c}\right)^{-1 / 2}\)
(b) Use the binomial theorem to show that if \(v \ll c\), this is approximately equal to
\(f_{R}=f_{S}\left(1-\frac{v}{c}\right)\)
(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, \(c=3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\).
Equation Transcription:
Text Transcription:
fR=fs(1-v/c)^½(1+v/c)^-½
v<<c
fR=fs(1-v/c)
c=3.00x10^8 m/s
ANSWER:
Solution 78P
(a) The frequency measured by the receiver is given by
…..(1)
Therefore, the given equation