(III) A certain atom emits light of frequency f 0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is Δ f / f 0 ≈ 2 3 k T / m c 2 ; assume m c 2 ≫ 3 k T . Evaluate Δ f / f 0 for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
(III) A certain atom emits light of frequency f 0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is Δ f / f 0 ≈ 2 3 k T / m c 2 ; assume m c 2 ≫ 3 k T . Evaluate Δ f / f 0 for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
(III) A certain atom emits light of frequency f0 when at rest. A monatomic gas composed of these atoms is at temperature T. Some of the gas atoms move toward and others away from an observer due to their random thermal motion. Using the rms speed of thermal motion, show that the fractional difference between the Doppler-shifted frequencies for atoms moving directly toward the observer and directly away from the observer is
Δ
f
/
f
0
≈
2
3
k
T
/
m
c
2
; assume
m
c
2
≫
3
k
T
. Evaluate
Δ
f
/
f
0
for a gas of hydrogen atoms at 550 K. [This “Doppler-broadening” effect is commonly used to measure gas temperature, such as in astronomy.]
A heater emits heater with wavelength 0.009 m.(a) Determine the frequency of the heater.Hz the heater is attached to a comet traveling away from the earth at a speed vse = 0.066c, where c is the speed of light. An observer is on a second comet that is also traveling away from the earth along the same line and in the same direction as the first comet at a speed voe = 0.056c.(b) Determine the ratio vso/c, where vso is the speed of the heater relative to the observer.vso/c =(c) What is the frequency of the emitted heater that would be measured by the observer? in Hz
If a sound with frequency fs is produced by a source traveling along a line with speed vs. If an observer is traveling with
speed v along the same line from the opposite direction toward the source, then the frequency of the sound heard by the
observer is
6-(C+₂)6
fo
where c is the speed of sound, about 332 m/s. (This is the Doppler effect.) Suppose that, at a particular moment, you are
in a train traveling at 42 m/s and accelerating at 1.6 m/s². A train is approaching you from the opposite direction on the
other track at 47 m/s, accelerating at 1.7 m/s², and sounds its whistle, which has a frequency of 438 Hz. At that instant,
what is the perceived frequency that you hear? (Round your answer to one decimal place.)
580.7
X Hz
How fast is it changing? (Round your answer to two decimal places.)
X Hz/s
5.90
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.