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Competition No. 262.
Two airplanes move in a straight line, one toward the other, at the same >uniform speed. The first airplane emits a signal from its radio
transmitter every 20 seconds, which is received by the second airplane
after 20 seconds minus 1/100,000 of a second. The question is: What is
the speed of the airplanes?
In article <10ajsn3$iu6p$2@dont-email.me>,
David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:
Competition No. 262.
Two airplanes move in a straight line, one toward the other, at the same
uniform speed. The first airplane emits a signal from its radio
transmitter every 20 seconds, which is received by the second airplane
after 20 seconds minus 1/100,000 of a second. The question is: What is
the speed of the airplanes?
Do you think it is supposed to mean that a signal is received every 20-1/100,000 seconds?
-- Richard
Do you think it is supposed to mean that a signal is received every 20-1/100,000 seconds?
https://archive.org/details/Sapere
Competition No. 262.
Two airplanes move in a straight line, one toward the other, at the same uniform speed. The first airplane emits a signal from its radio
transmitter every 20 seconds, which is received by the second airplane
after 20 seconds minus 1/100,000 of a second. The question is: What is
the speed of the airplanes?
.....
Another interesting aspect related to this question concerns the Doppler >effect on the radio communication.
If we have a SR-71 aircraft flying directly towards a ground-based radio >communication facility, at a ground-speed of 1000 m/s, and the craft >transmits using the military UHF Guard Band frequency of 243.0 MHz, then >what is the frequency offset of the signal received at the ground station?
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Strictly speaking, you need the relatistic Doppler shift where
the received frequency, f_r, is related to the source frequency
f_s by
f_r = f_s*sqrt((1+b)/(1-b))
where b = v/c and v is the relative speed of the source moving
*towards* the receiver.
Here, b = 1000/2.99792458x10^8 = 3.33564095 x 10^-6
and we are clearly in the classical regime. But, forging ahead
we get
f_r = f_s * 1.00000333 = 243 * 1.00000333
= 243.00081 MHz
The classical dilation factor 1 + b is pretty much
the same at this level of numerical precision.
Very good. Assuming a typical (for the era) and correctly tuned
heterodyne aeronautical receiver at the ground station, it will
demodulate the signal to the intermediate frequency with an offset of
about 810Hz. That's one reason aeronautical radio communications still
uses spectrally (and power) inefficient amplitude modulation in a wide >channel. It accommodates this effect without interference to the
adjacent channel and by including the unmodulated carrier and both upper
and lower sidebands. It allows recovery of the modulating audio, without
the offset having any adverse effect. More sophisticated modulations
schemes like UMTS (3G) and LTE (4G) have upper velocity limits built
into the specification partly because of Doppler effects and partly
because of handover timing requirements.
The Apollo command modules reach speeds roughly 10 times
the speed for the SR-71, but even this is well in the classical
domain.
I have to delve a deeper into what you say as my knowlege of
radio is rather limited. I have to dig out my copy of Paul
Nahin's "The Science of Radio" and refresh some basics before
diving deeper.