Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
10th Edition
ISBN: 9781337888745
Author: SERWAY, Raymond A., Jewett, John W.
Publisher: Cengage Learning
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Textbook Question
Chapter 36, Problem 36AP
Figure P36.35 shows a radio-wave transmitter and a receiver separated by a distance d and both a distance h above the ground. The receiver can receive signals both directly from the transmitter and indirectly from signals that reflect from the ground. Assume the ground is level between the transmitter and receiver and a 180° phase shift occurs upon reflection. Determine the longest wavelengths that interfere (a) constructively and (b) destructively.
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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
Bundle: Physics for Scientists and Engineers, Volume 2, Loose-leaf Version, 10th + WebAssign Printed Access Card, Single-Term
Ch. 36.2 - Which of the following causes the fringes in a...Ch. 36.3 - Using Figure 36.6 as a model, sketch the...Ch. 36.5 - One microscope slide is placed on top of another...Ch. 36 - Two slits are separated by 0.320 mm. A beam of...Ch. 36 - Why is the following situation impossible? Two...Ch. 36 - A laser beam is incident on two slits with a...Ch. 36 - In a Youngs double-slit experiment, two parallel...Ch. 36 - Light of wavelength 620 nm falls on a double slit,...Ch. 36 - Light with wavelength 442 nm passes through a...Ch. 36 - A student holds a laser that emits light of...
Ch. 36 - A student holds a laser that emits light of...Ch. 36 - Coherent light rays of wavelength strike a pair...Ch. 36 - In Figure P36.10 (not to scale), let L = 1.20 m...Ch. 36 - You are working in an optical research laboratory....Ch. 36 - You are operating a new radio telescope that has...Ch. 36 - In the double-slit arrangement of Figure P36.13, d...Ch. 36 - Monochromatic light of wavelength is incident on...Ch. 36 - Prob. 15PCh. 36 - Show that the distribution of intensity in a...Ch. 36 - Green light ( = 546 nm) illuminates a pair of...Ch. 36 - Monochromatic coherent light of amplitude E0 and...Ch. 36 - A material having an index of refraction of 1.30...Ch. 36 - A soap bubble (n = 1.33) floating in air has the...Ch. 36 - A film of MgF2 (n = 1.38) having thickness 1.00 ...Ch. 36 - An oil film (n = 1.45) floating on water is...Ch. 36 - When a liquid is introduced into the air space...Ch. 36 - You are working as an expert witness for an...Ch. 36 - Astronomers observe the chromosphere of the Sun...Ch. 36 - A lens made of glass (ng = 1.52) is coated with a...Ch. 36 - Mirror M1 in Figure 36.13 is moved through a...Ch. 36 - Radio transmitter A operating at 60.0 MHz is 10.0...Ch. 36 - In an experiment similar to that of Example 36.1,...Ch. 36 - In the What If? section of Example 36.2, it was...Ch. 36 - Two coherent waves, coming from sources at...Ch. 36 - Raise your hand and hold it flat. Think of the...Ch. 36 - In a Youngs double-slit experiment using light of...Ch. 36 - Review. A flat piece of glass is held stationary...Ch. 36 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 36 - Figure P36.35 shows a radio-wave transmitter and a...Ch. 36 - In a Newtons-rings experiment, a plano-convex...Ch. 36 - Measurements are made of the intensity...Ch. 36 - A plano-concave lens having index of refraction...Ch. 36 - Why is the following situation impossible? A piece...Ch. 36 - Interference fringes are produced using Lloyds...Ch. 36 - A plano-convex lens has index of refraction n. The...Ch. 36 - Prob. 43APCh. 36 - Prob. 44APCh. 36 - Astronomers observe a 60.0-MHz radio source both...Ch. 36 - Prob. 46CPCh. 36 - Our discussion of the techniques for determining...Ch. 36 - The condition for constructive interference by...Ch. 36 - Both sides of a uniform film that has index of...Ch. 36 - Slit 1 of a double-slit is wider than slit 2 so...
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Spectra Interference: Crash Course Physics #40; Author: CrashCourse;https://www.youtube.com/watch?v=-ob7foUzXaY;License: Standard YouTube License, CC-BY