Homework Help is Here – Start Your Trial Now!
Science
Physics
(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?

(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question
(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?
Transcribed Image Text:(a) Determine the Fourier transform F(k) of the rectangular function f(x) = 1 for -a/2 ≤ x ≤a/2 f(x) = 0 elsewhere (b) What is the smallest k value for which F(k)=0? This defines the central peak width W. How does W changes if a is halved? (c) Plot F(k) versus k (use either Python, Matlab, Mathematica, Wolfram Alpha, or sketch by hand). Find the smallest value kmin of k such as F(kmin)= F(k=0)/10. This defines how far you have to go in k to have a good approximation of the rectangular function. Qualitatively, how does kmin evolves with a?
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS