Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 16, Problem 26P
(a)
To determine
The effect on the speed of the wave when it moves through air at
(b)
To determine
The effect on the frequency of the sound wave when it moves through the air at
(c)
To determine
The effect on the wavelength of the sound wave when the it moves through air at
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
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[2 marks]
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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)
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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.
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v=t+x.
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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
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Chapter 16 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 16.1 - Prob. 16.1QQCh. 16.2 - A sinusoidal wave of frequency f is traveling...Ch. 16.2 - The amplitude of a wave is doubled, with no other...Ch. 16.3 - Suppose you create a pulse by moving the free end...Ch. 16.4 - Which of the following, taken by itself, would be...Ch. 16.6 - If you blow across the top of an empty soft-drink...Ch. 16.8 - A vibrating guitar string makes very little sound...Ch. 16.8 - Increasing the intensity of a sound by a factor of...Ch. 16.9 - Consider detectors of water waves at three...Ch. 16.9 - You stand on a platform at a train station and...
Ch. 16.9 - An airplane flying with a constant velocity moves...Ch. 16 - A seismographic station receives S and P waves...Ch. 16 - Two points A and B on the surface of the Earth are...Ch. 16 - You are working for a plumber who is laying very...Ch. 16 - Prob. 4PCh. 16 - When a particular wire is vibrating with a...Ch. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - A sinusoidal wave traveling in the negative x...Ch. 16 - Prob. 9PCh. 16 - Prob. 10PCh. 16 - Prob. 11PCh. 16 - Prob. 12PCh. 16 - Tension is maintained in a string as in Figure...Ch. 16 - Prob. 14PCh. 16 - Transverse waves are being generated on a rope...Ch. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - A two-dimensional water wave spreads in circular...Ch. 16 - A horizontal string can transmit a maximum power...Ch. 16 - Prob. 20PCh. 16 - Show that the wave function y = eb(x vt) is a...Ch. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - Prob. 25PCh. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - Prob. 29PCh. 16 - Prob. 30PCh. 16 - The intensity of a sound wave at a fixed distance...Ch. 16 - Prob. 32PCh. 16 - The power output of a certain public-address...Ch. 16 - A fireworks rocket explodes at a height of 100 m...Ch. 16 - You are working at an open-air amphitheater, where...Ch. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - Submarine A travels horizontally at 11.0 m/s...Ch. 16 - Prob. 39PCh. 16 - Prob. 40PCh. 16 - Review. A block with a speaker bolted to it is...Ch. 16 - Prob. 42PCh. 16 - Prob. 43APCh. 16 - Prob. 44APCh. 16 - Prob. 45APCh. 16 - Prob. 46APCh. 16 - A sinusoidal wave in a string is described by the...Ch. 16 - Prob. 48APCh. 16 - A wire of density is tapered so that its...Ch. 16 - Prob. 50APCh. 16 - Prob. 51APCh. 16 - A train whistle (f = 400 Hz) sounds higher or...Ch. 16 - Review. A 150-g glider moves at v1 = 2.30 m/s on...Ch. 16 - Prob. 54APCh. 16 - Prob. 55APCh. 16 - Prob. 56APCh. 16 - Prob. 57CPCh. 16 - Assume an object of mass M is suspended from the...Ch. 16 - Prob. 59CPCh. 16 - Prob. 60CP
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