Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 36.5, Problem 36.5CE
To determine
The reason for not produce spectrum by Young’s double slit experiment with the help of well separated spectral lines.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 36 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 36.2 - Prob. 36.1CECh. 36.3 - Prob. 36.2CECh. 36.4 - Prob. 36.3CECh. 36.5 - Prob. 36.4CECh. 36.5 - Prob. 36.5CECh. 36 - Many circular apertures are adjustable, such as...Ch. 36 - Many of the images we regularly look at are...Ch. 36 - The hydrogen line at 1420.4 MHz corresponds to the...Ch. 36 - Prob. 4PQCh. 36 - Estimate the diffraction-limited resolution of the...
Ch. 36 - Prob. 6PQCh. 36 - Prob. 7PQCh. 36 - Prob. 8PQCh. 36 - Prob. 9PQCh. 36 - Prob. 10PQCh. 36 - Prob. 11PQCh. 36 - Prob. 12PQCh. 36 - Prob. 13PQCh. 36 - Prob. 14PQCh. 36 - Prob. 15PQCh. 36 - Prob. 16PQCh. 36 - Prob. 17PQCh. 36 - Prob. 18PQCh. 36 - Prob. 19PQCh. 36 - Prob. 20PQCh. 36 - Prob. 21PQCh. 36 - Prob. 22PQCh. 36 - Prob. 23PQCh. 36 - Prob. 24PQCh. 36 - Light of wavelength 566 nm is incident on a...Ch. 36 - Prob. 26PQCh. 36 - Prob. 27PQCh. 36 - Prob. 28PQCh. 36 - Prob. 29PQCh. 36 - Prob. 30PQCh. 36 - A light source emits a mixture of wavelengths from...Ch. 36 - Prob. 32PQCh. 36 - Prob. 33PQCh. 36 - Prob. 34PQCh. 36 - Prob. 35PQCh. 36 - Prob. 36PQCh. 36 - Prob. 37PQCh. 36 - Prob. 38PQCh. 36 - Prob. 39PQCh. 36 - Prob. 40PQCh. 36 - Prob. 41PQCh. 36 - Prob. 42PQCh. 36 - Prob. 43PQCh. 36 - Prob. 44PQCh. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - CASE STUDY Michelsons interferometer played an...Ch. 36 - Prob. 47PQCh. 36 - Prob. 48PQCh. 36 - Problems 49 and 50 are paired. C Optical flats are...Ch. 36 - Optical flats are flat pieces of glass used to...Ch. 36 - Prob. 51PQCh. 36 - Prob. 52PQCh. 36 - Figure P36.53 shows two thin glass plates...Ch. 36 - Viewed from above, a thin film of motor oil with...Ch. 36 - Newtons rings, discovered by Isaac Newton, are an...Ch. 36 - Prob. 56PQCh. 36 - What is the radius of the beam of an argon laser...Ch. 36 - Prob. 58PQCh. 36 - A diffraction grating with 428 rulings per...Ch. 36 - How many rulings must a diffraction grating have...Ch. 36 - Prob. 61PQCh. 36 - White light is incident on a diffraction grating...Ch. 36 - X-rays incident on a crystal with planes of atoms...Ch. 36 - Prob. 64PQCh. 36 - Prob. 65PQCh. 36 - Prob. 66PQCh. 36 - The fringe width b is defined as the distance...Ch. 36 - The fringe width is defined as the distance...Ch. 36 - Prob. 69PQ
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