EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 8220100546310
Author: Jewett
Publisher: CENGAGE L
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Textbook Question
Chapter 18, Problem 18.43P
An air column in a glass tube is open at one end and closed at the other by a movable piston. The air in the tube is warmed above room temperature, and a 384-Hz tuning fork is held at the open end. Resonance is heard when the piston is at a distance d1 = 22.8 cm from the open end and again when it is at a distance d2= 68.3 cm from the open end. (a) What speed of sound is implied by these data? (b) How far from the open end will the piston be when the next resonance is heard?
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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]
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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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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,
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[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
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Chapter 18 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
Ch. 18 - Prob. 18.1QQCh. 18 - Consider the waves in Figure 17.8 to be waves on a...Ch. 18 - When a standing wave is set up on a string fixed...Ch. 18 - Prob. 18.4QQCh. 18 - Balboa Park in San Diego has an outdoor organ....Ch. 18 - In figure OQ18.1 (page 566), a sound wave of...Ch. 18 - A string of length L, mass pet unit length , and...Ch. 18 - In Example 18.1, we investigated an oscillator at...Ch. 18 - Prob. 18.4OQCh. 18 - A flute has a length of 58.0 cm. If the speed of...
Ch. 18 - When two tuning forks are sounded at the same...Ch. 18 - A tuning fork is known to vibrate with frequency...Ch. 18 - An archer shoots an arrow horizontally from the...Ch. 18 - As oppositely moving pulses of the same shape (one...Ch. 18 - Prob. 18.10OQCh. 18 - Suppose all six equal-length strings of an...Ch. 18 - Assume two identical sinusoidal waves are moving...Ch. 18 - Prob. 18.1CQCh. 18 - When two waves interfere constructively or...Ch. 18 - Prob. 18.3CQCh. 18 - What limits the amplitude of motion of a real...Ch. 18 - Prob. 18.5CQCh. 18 - An airplane mechanic notices that the sound from a...Ch. 18 - Despite a reasonably steady hand, a person often...Ch. 18 - Prob. 18.8CQCh. 18 - Does the phenomenon of wave interference apply...Ch. 18 - Two waves are traveling in the same direction...Ch. 18 - Two wave pulses A and B are moving in opposite...Ch. 18 - Two waves on one string are described by the wave...Ch. 18 - Two pulses of different amplitudes approach each...Ch. 18 - A tuning fork generates sound waves with a...Ch. 18 - The acoustical system shown in Figure OQ18.1 is...Ch. 18 - Two pulses traveling on the same string are...Ch. 18 - Two identical loudspeakers are placed on a wall...Ch. 18 - Two traveling sinusoidal waves are described by...Ch. 18 - Why is the following situation impossible? Two...Ch. 18 - Two sinusoidal waves on a string are defined by...Ch. 18 - Two identical sinusoidal waves with wavelengths of...Ch. 18 - Two identical loudspeakers 10.0 m apart are driven...Ch. 18 - Prob. 18.14PCh. 18 - Two sinusoidal waves traveling in opposite...Ch. 18 - Verify by direct substitution that the wave...Ch. 18 - Two transverse sinusoidal waves combining in a...Ch. 18 - A standing wave is described by the wave function...Ch. 18 - Two identical loudspeakers are driven in phase by...Ch. 18 - Prob. 18.20PCh. 18 - A string with a mass m = 8.00 g and a length L =...Ch. 18 - The 64.0-cm-long string of a guitar has a...Ch. 18 - The A string on a cello vibrates in its first...Ch. 18 - A taut string has a length of 2.60 m and is fixed...Ch. 18 - A certain vibrating string on a piano has a length...Ch. 18 - A string that is 30.0 cm long and has a mass per...Ch. 18 - In the arrangement shown in Figure P18.27, an...Ch. 18 - In the arrangement shown in Figure P17.14, an...Ch. 18 - Review. A sphere of mass M = 1.00 kg is supported...Ch. 18 - Review. A sphere of mass M is supported by a...Ch. 18 - Prob. 18.31PCh. 18 - Review. A solid copper object hangs at the bottom...Ch. 18 - Prob. 18.33PCh. 18 - The Bay of Fundy, Nova Scotia, has the highest...Ch. 18 - An earthquake can produce a seiche in a lake in...Ch. 18 - High-frequency sound can be used to produce...Ch. 18 - Prob. 18.37PCh. 18 - Prob. 18.38PCh. 18 - Calculate the length of a pipe that has a...Ch. 18 - The overall length of a piccolo is 32.0 cm. The...Ch. 18 - The fundamental frequency of an open organ pipe...Ch. 18 - Prob. 18.42PCh. 18 - An air column in a glass tube is open at one end...Ch. 18 - Prob. 18.44PCh. 18 - Prob. 18.45PCh. 18 - A shower stall has dimensions 86.0 cm 86.0 cm ...Ch. 18 - Prob. 18.47PCh. 18 - Prob. 18.48PCh. 18 - As shown in Figure P17.27, water is pumped into a...Ch. 18 - As shown in Figure P17.27, water is pumped into a...Ch. 18 - Two adjacent natural frequencies of an organ pipe...Ch. 18 - Why is the following situation impossible? A...Ch. 18 - A student uses an audio oscillator of adjustable...Ch. 18 - An aluminum rod is clamped one-fourth of the way...Ch. 18 - Prob. 18.55PCh. 18 - Prob. 18.56PCh. 18 - In certain ranges of a piano keyboard, more than...Ch. 18 - Prob. 18.58PCh. 18 - Review. A student holds a tuning fork oscillating...Ch. 18 - An A-major chord consists of the notes called A,...Ch. 18 - Suppose a flutist plays a 523-Hz C note with first...Ch. 18 - A pipe open at both ends has a fundamental...Ch. 18 - Prob. 18.63APCh. 18 - Two strings are vibrating at the same frequency of...Ch. 18 - Prob. 18.65APCh. 18 - A 2.00-m-long wire having a mass of 0.100 kg is...Ch. 18 - The fret closest to the bridge on a guitar is 21.4...Ch. 18 - Prob. 18.68APCh. 18 - A quartz watch contains a crystal oscillator in...Ch. 18 - Review. For the arrangement shown in Figure...Ch. 18 - Prob. 18.71APCh. 18 - Two speakers are driven by the same oscillator of...Ch. 18 - Review. Consider the apparatus shown in Figure...Ch. 18 - Review. The top end of a yo-yo string is held...Ch. 18 - On a marimba (Fig. P18.75), the wooden bar that...Ch. 18 - A nylon siring has mass 5.50 g and length L = 86.0...Ch. 18 - Two train whistles have identical frequencies of...Ch. 18 - Review. A loudspeaker at the front of a room and...Ch. 18 - Prob. 18.79APCh. 18 - Prob. 18.80APCh. 18 - Prob. 18.81APCh. 18 - A standing wave is set up in a string of variable...Ch. 18 - Two waves are described by the wave functions...Ch. 18 - Prob. 18.84APCh. 18 - Review. A 12.0-kg object hangs in equilibrium from...Ch. 18 - Review. An object of mass m hangs in equilibrium...Ch. 18 - Review. Consider the apparatus shown in Figure...Ch. 18 - Prob. 18.88CP
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