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(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
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Physics for Scientists and Engineers with Modern Physics
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- The light from a heated atomic gas is shifted in frequency because of the random thermal motion of light-emitting atoms toward or away from an observer. Estimate the fractional Doppler shift (f/f0), assuming that light of frequency f0 is emitted in the rest frame of each atom, that the light-emitting atoms are iron atoms in a star at temperature 6000 K, and that the atoms are moving relative to an observer with the mean speed =8kBTm Must we use the relativistic Doppler shift formulas f=f01/c1/c for this calculation? Such thermal Doppler shifts are measurable and are used to determine stellar surface temperatures.arrow_forwardGeneral Relativity Consider a spherical blackbody of constant temperature and mass M whose surface lies at radial coordinate r = R. An observer located at the surface of the sphere and a distant observer both measure the blackbody radiation given off by the sphere.Both observers use Wien's law, the below equation, to determine the blackbody's temperature. Show that 2GM T = T/1 Rc2arrow_forwardIf a sound with frequency f, is produced by a source traveling along a line with speed vg and 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 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 44 m/s and accelerating at 1.6 m/s2. A train is approaching you from the opposite direction on the other track at 48 m/s, accelerating at 1.9 m/s?, and sounds its whistle, which has a frequency of 428 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.) Hz How fast is it changing? (Round your answer to two decimal places.) Hz/sarrow_forward
- A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.3 days. The average brightness of this star is 4.0 and its brightness changes by ±0.45. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 4.0 +0.45 sin (a) Find the rate of change of the brightness after t days. dB dt (b) Find, correct to two decimal places, the rate of increase after five days. dB dtarrow_forwardIf a sound with frequency f, is produced by a source traveling along a line with speed v, and an observer straveling 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 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 37 m/s and accelerating at 1.7 m/s². A train is approaching you from the opposite direction on the other track at 43 m/s, accelerating at 1.8 m/s2, and sounds its whistle, which has a frequency of 435 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.) Hz How fast is it changing? (Round your answer to two decimal places.) Hz/sarrow_forwardA galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.arrow_forward
- 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 Vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is c + V. 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 33 m/s and accelerating at 1.3 m/s². A train is approaching you from the opposite direction on the other track at 35 m/s, accelerating at 1.6 m/s2, and sounds its whistle, which has a frequency of 468 Hz. At that instant, what is the perceived frequency that you hear? (Round your answer to one decimal place.) Hz How fast is it changing? (Round your answer to two decimal places.) Hz/sarrow_forwardA light beam with the wavelength of 660 nm (AA) is created by a spaceship (A), is observed as its wavelength is 924 nm (Aobserved). Another spaceship (B) is observed by Earth as it is receding with the speed of 0.7c (VB,Earth). The angular distance between these two spaceship is 90 degrees for an observer at Earth. Find the speed of the spaceship B for an observer located at the spaceship A (VBA). M = 660nm VB,A = ? Aobserved = 924nm VB,Earth = 0.7c Barrow_forwardTwo cars A & B are driving away from each other and sounding their horns. You are the driver of car B which is travelling at a speed of 23.6m/s and you measured the horn of the other car to be sounded at 885HZ, which is travelling at a speed of 27.9m/s. Speed of sound is 340m/s. Calculate the following: a) Speed of the observer in m/s %3D (0.5 mark) b) Speed of the source in m/s %3D (0.5 mark) c) frequency of the source (original) in hertz (1.5 mark) d) How much does the frequency of the source decreased (A) in hertz =arrow_forward
- The spectrum of a sun-like star is monitored and it is noticed that a spectral absorption line of wavelength A = 589 nm shifts periodically with a period equal to 10 days. The amplitude of the shift AX = ±1 × 10¬4 nm. The sun-like star has a mass M, = 2 × 1030 kg. Assuming that the periodic shifting of spectral lines is due to an unseen orbiting planet, estimate its mass. Express your answer in Earth massesarrow_forwardThe frequency of light reaching Earth froma particular galaxy is 15% lower than the frequency the light hadwhen it was emitted. (a) Is this galaxy moving toward or awayfrom Earth? Explain. (b) What is the speed of this galaxy relativeto the Earth? Give your answer as a fraction of the speed of light.arrow_forwardA light source and an observer approach each other with relative speed v 0.9c, and the frequency f'measured by the observer is f'= 100 MHz, what is the frequency fof the source? 58 MHz O 33 MHz 23 МHz 45 MHz 100 MHzarrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
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