Explanation Consider a source of light and the receiver; the velocity of receiver is v and the velocity of light is c . The source emits n waves during time interval T . The receiver is approaching the rest source; so the relative velocity of light with respect to receiver is v . The length of wave train is c T − v T and there are n waves emitted during interval T . Write the expression of wavelength: λ = c T − v T n Here, λ is the wavelength, T is time interval, v is the relative velocity, c is the velocity of light. Write the expression of frequency: f = c λ Substitute c T − v T n for λ in above expression. f = c n c T − v T (I) Here, f is the frequency of light. The source in rest emits n waves of frequency f 0 during proper time T 0 . Write the expression for n : n = f 0 T 0 (II) Here, n is the number of waves, f 0 is the natural frequency and T 0 is the proper time. Write the relation between proper time and time interval: T 0 = T γ Here, γ is the relativistic factor. Substitute T γ for T 0 in equation (II) n = f 0 T γ (III) Substitute f 0 T γ for n in equation (I). f = c ( f 0 T γ ) c T − v T = ( c f 0 T γ ) ⋅ 1 c T ( 1 − v c ) = 1 ( 1 − v c ) ⋅ f 0 γ Further substitute 1 ( 1 − v 2 c 2 ) for γ in above expression

Modern Physics for Scientists and Engineers

4th Edition

ISBN: 9781133103721

Author: Stephen T. Thornton, Andrew Rex

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force betwe…

Question

Chapter 2, Problem 49P

To determine

To derive equation (2.32) when the source is fixed and the receiver approaches it with velocity v.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 48P

Chapter 2, Problem 50P

Students have asked these similar questions

No chatgpt pls will upvote

a cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?

Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.

Chapter 2 Solutions

Modern Physics for Scientists and Engineers

Ch. 2 - Michelson used the motion of the Earth around the...Ch. 2 - If you wanted to set out today to find the effects...Ch. 2 - Prob. 3Q Ch. 2 - Prob. 4Q Ch. 2 - Prob. 5Q Ch. 2 - Prob. 6Q Ch. 2 - Prob. 7Q Ch. 2 - Prob. 8Q Ch. 2 - Devise a system for you and three colleagues, at...Ch. 2 - In the experiment to verify time dilation by...

Ch. 2 - Can you think of an experiment to verify length...Ch. 2 - Would it be easier to perform the muon decay...Ch. 2 - On a spacetime diagram, can events above t = 0 but...Ch. 2 - Prob. 14Q Ch. 2 - What would be a suitable name for events connected...Ch. 2 - Prob. 16Q Ch. 2 - Prob. 17Q Ch. 2 - Explain how in the twin paradox, we might arrange...Ch. 2 - In each of the following pairs, which is the more...Ch. 2 - Prob. 20Q Ch. 2 - Prob. 21Q Ch. 2 - A salesman driving a very fast car was arrested...Ch. 2 - A salesman driving a very fast car was arrested...Ch. 2 - Show that the form of Newtons second law is...Ch. 2 - Prob. 2P Ch. 2 - Prob. 3P Ch. 2 - A swimmer wants to swim straight across a river...Ch. 2 - Prob. 5P Ch. 2 - Prob. 6P Ch. 2 - Prob. 7P Ch. 2 - Prob. 8P Ch. 2 - Prove that the constancy of the speed of light...Ch. 2 - Prob. 10P Ch. 2 - Prob. 11P Ch. 2 - Prob. 12P Ch. 2 - Two events occur in an inertial system K as...Ch. 2 - Is there a frame K in which the two events...Ch. 2 - Prob. 15P Ch. 2 - An event occurs in system K at x = 2 m, y = 3.5 m,...Ch. 2 - Prob. 17P Ch. 2 - Prob. 18P Ch. 2 - A rocket ship carrying passengers blasts off to go...Ch. 2 - Prob. 20P Ch. 2 - Particle physicists use particle track detectors...Ch. 2 - The Apollo astronauts returned from the moon under...Ch. 2 - A clock in a spaceship is observed to run at a...Ch. 2 - A spaceship of length 40 m at rest is observed to...Ch. 2 - Prob. 25P Ch. 2 - A mechanism on Earth used to shoot down...Ch. 2 - Prob. 27P Ch. 2 - Imagine that in another universe the speed of...Ch. 2 - Prob. 29P Ch. 2 - Prob. 30P Ch. 2 - Prob. 31P Ch. 2 - A proton and an antiproton are moving toward each...Ch. 2 - Imagine the speed of light in another universe to...Ch. 2 - Prob. 34P Ch. 2 - Three galaxies are aligned along an axis in the...Ch. 2 - Prob. 36P Ch. 2 - Prob. 37P Ch. 2 - Consider a reference system placed at the U.S....Ch. 2 - Prob. 39P Ch. 2 - Prob. 40P Ch. 2 - Use the Lorentz transformation to prove that s2 =...Ch. 2 - Prob. 42P Ch. 2 - Prove that for a spacelike interval, two events...Ch. 2 - Given two events, (x1, t1) and (x2, t2), use a...Ch. 2 - Prob. 45P Ch. 2 - Consider a fixed and a moving system with their...Ch. 2 - Prob. 47P Ch. 2 - An astronaut is said to have tried to get out of a...Ch. 2 - Prob. 49P Ch. 2 - Do the complete derivation for Equation (2.33)...Ch. 2 - A spacecraft traveling out of the solar system at...Ch. 2 - Prob. 52P Ch. 2 - Prob. 53P Ch. 2 - Prob. 54P Ch. 2 - Newtons second law is given by F=dp/dt. If the...Ch. 2 - Use the result of the previous problem to show...Ch. 2 - Prob. 57P Ch. 2 - Prob. 58P Ch. 2 - A particle having a speed of 0.92c has a momentum...Ch. 2 - A particle initially has a speed of 0.5c. At what...Ch. 2 - Prob. 61P Ch. 2 - Prob. 62P Ch. 2 - Prob. 63P Ch. 2 - Prob. 64P Ch. 2 - Prob. 65P Ch. 2 - Prob. 66P Ch. 2 - Prob. 67P Ch. 2 - Prob. 68P Ch. 2 - Prob. 69P Ch. 2 - Prob. 70P Ch. 2 - What is the speed of an electron when its kinetic...Ch. 2 - Prob. 72P Ch. 2 - Prob. 73P Ch. 2 - Prob. 74P Ch. 2 - Prob. 75P Ch. 2 - Calculate the energy needed to accelerate a...Ch. 2 - Prob. 77P Ch. 2 - Prob. 78P Ch. 2 - Prob. 79P Ch. 2 - Prob. 80P Ch. 2 - The Large Hadron Collider at Europes CERN facility...Ch. 2 - What is the kinetic energy of (a) an electron...Ch. 2 - A muon has a mass of 106 MeV/c2. Calculate the...Ch. 2 - Prob. 84P Ch. 2 - The reaction 2H + 3H → n + 4He is one of the...Ch. 2 - Instead of one positive charge outside a...Ch. 2 - Prob. 87P Ch. 2 - Show that the following form of Newton’s second...Ch. 2 - Prob. 89P Ch. 2 - For the twins Frank and Mary described in Section...Ch. 2 - Frank and Mary are twins. Mary jumps on a...Ch. 2 - A police radar gun operates at a frequency of 10.5...Ch. 2 - Prob. 93P Ch. 2 - Prob. 94P Ch. 2 - A proton moves with a speed of 0.90c. Find the...Ch. 2 - A high-speed K0 meson is traveling at a speed of...Ch. 2 - Prob. 97P Ch. 2 - The International Space Federation constructs a...Ch. 2 - Prob. 99P Ch. 2 - Prob. 100P Ch. 2 - A spaceship is coming directly toward you while...Ch. 2 - Quasars are among the most distant objects in the...Ch. 2 - One possible decay mode of the neutral kaon is K0...Ch. 2 - Prob. 104P Ch. 2 - Prob. 105P Ch. 2 - Small differences in the wavelengths in the sun’s...

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.

To derive equation (2.32) when the source is fixed and the receiver approaches it with velocity v .

Solution Summary: The author explains the equation (2.32) derived when the source is fixed and the receiver approaches it with velocity v.

Concept explainers

To derive equation (2.32) when the source is fixed and the receiver approaches it with velocity v.

Want to see the full answer?

Chapter 2 Solutions