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How is the relativistic Doppler effect different from the classical Doppler effect?
The relativistic Doppler effect takes into account the special relativity concept of time dilation and also does not require a medium of propagation to be used as a point of reference (light does not require a medium for propagation).
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Section summary
- With classical velocity addition, velocities add like regular numbers in one-dimensional motion:
, where
is the velocity between two observers,
is the velocity of an object relative to one observer, and
is the velocity relative to the other observer.
- Velocities cannot add to be greater than the speed of light. Relativistic velocity addition describes the velocities of an object moving at a relativistic speed:
- An observer of electromagnetic radiation sees
relativistic Doppler effects if the source of the radiation is moving relative to the observer. The wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves toward the observer. The shifted wavelength is described by the equation
is the observed wavelength,
is the source wavelength, and
is the relative velocity of the source to the observer.
Conceptual questions
Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that
is larger for motion away?
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All galaxies farther away than about
exhibit a red shift in their emitted light that is proportional to distance, with those farther and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion? (Hint: At these large distances, it is space itself that is expanding, but the effect on light is the same.)
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Problems&Exercises
Suppose a spaceship heading straight towards the Earth at
can shoot a canister at
relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?
(a)
(b)
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If a spaceship is approaching the Earth at
and a message capsule is sent toward it at
relative to the Earth, what is the speed of the capsule relative to the ship?
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(a) Suppose the speed of light were only
. A jet fighter moving toward a target on the ground at
shoots bullets, each having a muzzle velocity of
. What are the bullets’ velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.
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If a galaxy moving away from the Earth has a speed of
and emits
light characteristic of hydrogen (the most common element in the universe). (a) What wavelength would we observe on the Earth? (b) What type of electromagnetic radiation is this? (c) Why is the speed of the Earth in its orbit negligible here?
a)
b) red
c)
(negligible)
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A space probe speeding towards the nearest star moves at
and sends radio information at a broadcast frequency of 1.00 GHz. What frequency is received on the Earth?
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If two spaceships are heading directly towards each other at
, at what speed must a canister be shot from the first ship to approach the other at
as seen by the second ship?
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Two planets are on a collision course, heading directly towards each other at
. A spaceship sent from one planet approaches the second at
as seen by the second planet. What is the velocity of the ship relative to the first planet?
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When a missile is shot from one spaceship towards another, it leaves the first at
and approaches the other at
. What is the relative velocity of the two ships?
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Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive 1900 nm electromagnetic radiation and know that it was 1875 nm when emitted by the hydrogen gas. What is the speed of the gas?
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A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.
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Prove that for any relative velocity
between two observers, a beam of light sent from one to the other will approach at speed
(provided that
is less than
, of course).
, so
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Show that for any relative velocity
between two observers, a beam of light projected by one directly away from the other will move away at the speed of light (provided that
is less than
, of course).
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(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy
ly away is receding from us at 0.
, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at
, as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)
a)
b)
c)
(all to sufficient digits to show effects)
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Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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