COLLEGE PHYSICS
2nd Edition
ISBN: 9781711470832
Author: OpenStax
Publisher: XANEDU
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Textbook Question
Chapter 17, Problem 78PE
(a) Find the size of the smallest detail observable in human tissue with 20.0-MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00 cm is needed)? (c) What is the wavelength of such ultrasound in 0°C air?
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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 17 Solutions
COLLEGE PHYSICS
Ch. 17 - How do sound vibrations of atoms differ from...Ch. 17 - When sound passes from one medium to another where...Ch. 17 - Six members at a synchronized swim team weal...Ch. 17 - A community is concerned about a plan to bring...Ch. 17 - Is the Doppler shift real or just a sensory...Ch. 17 - Due to eficiency considerations related to its bow...Ch. 17 - When you hear a sonic boom, you often cannot see...Ch. 17 - How does an unamplified guitar produce sounds so...Ch. 17 - You are given two wind instruments of identical...Ch. 17 - What is the difference between an overtone and a...
Ch. 17 - Why can a hearing test show that your threshold of...Ch. 17 - If audible sound follows a rule of thumb similar...Ch. 17 - Elephants and whales are known to use infrasound...Ch. 17 - It is more difficult to obtain a high—resolution...Ch. 17 - Suppose you read mat 210dB ultrasound is being...Ch. 17 - When poked by a spear, an operatic soprano lets...Ch. 17 - What frequency sound has a 0.10m wavelength when...Ch. 17 - Calculate the speed of sound on a day when a 1500...Ch. 17 - Prob. 4PECh. 17 - Show mat the speed of sound in 20.0°C air is 343...Ch. 17 - Air temperature in the Sahara Desert can reach...Ch. 17 - Dolphins make sounds in air and water. What is the...Ch. 17 - A sonar echo returns to a submarine 1.20 s after...Ch. 17 - (a) If a submarine’s sonar can measure echo times...Ch. 17 - A physicist a1 a fireworks display times the lag...Ch. 17 - Prob. 11PECh. 17 - What is the intensity in watts per meter squared...Ch. 17 - The warning tag on a lawn mower states that it...Ch. 17 - A sound wave traveling in 20°C air has a pressure...Ch. 17 - What intensity level does the sound in the...Ch. 17 - What sound intensity level in dB is produced by...Ch. 17 - Show that an intensity of 1012 W/m2 is the same as...Ch. 17 - (a) What is the decibel level of a sound that is...Ch. 17 - (a) What is the intensity of a sound that has a...Ch. 17 - (a) How much more intense is a sound that has a...Ch. 17 - People with good hearing can perceive sounds as...Ch. 17 - If a large housefly 3.0 m away from you makes a...Ch. 17 - Ten cars in a circle at a boom box competition...Ch. 17 - The amplitude of a sound wave is measured in terms...Ch. 17 - If a sound intensity level of 0 dB at 1000 Hz...Ch. 17 - An 8hour exposure to a sound intensity level of...Ch. 17 - (a) Ear trumpets were never very common, but they...Ch. 17 - Sound is more effectively transmitted into a...Ch. 17 - Loudspeakers can produce intense sounds with...Ch. 17 - (a) What frequency is received by a person...Ch. 17 - (a) At an air show a jet flies directly toward the...Ch. 17 - What frequency is received by a mouse just before...Ch. 17 - A spectator at a parade receives an 888-Hz tone...Ch. 17 - A commuter train blows its 200Hz horn as it...Ch. 17 - Can you perceive the shift in frequency produced...Ch. 17 - Two eagles fly directly toward one another. The...Ch. 17 - What is the minimum speed at which a source must...Ch. 17 - A “showy" custom—built car has two brass horns...Ch. 17 - What beat frequencies will be present: (a) If the...Ch. 17 - What beat frequencies result if a piano hammer...Ch. 17 - A piano tuner hears a heat every 2.00 s when...Ch. 17 - (a) What is the fundamental frequency of a...Ch. 17 - If a wind instrument, such as a tuba, has a...Ch. 17 - What are the first three overtones of a bassoon...Ch. 17 - How long must a fiute be in order to have a...Ch. 17 - What length should an oboe have to produce a...Ch. 17 - What is the length of a tube that has a...Ch. 17 - (a) Find the length of an organ pipe closed at one...Ch. 17 - By what fraction will the frequencies produced by...Ch. 17 - Prob. 50PECh. 17 - Calculate the first overtone in an ear canal,...Ch. 17 - Prob. 52PECh. 17 - (a) Students in a physics lab are asked to find...Ch. 17 - What frequencies will a 1.80-m—long tube produce...Ch. 17 - The factor of 1012 in the range of intensities to...Ch. 17 - The frequencies to which the ear responds vary by...Ch. 17 - What are the closest frequencies to 500 Hz that an...Ch. 17 - Can the average person tell that a 2002-Hz sound...Ch. 17 - If your radio is producing an average sound...Ch. 17 - Can you tell that your roommate turned up the...Ch. 17 - Prob. 61PECh. 17 - What sound intensity levels must sounds of...Ch. 17 - What is me approximate sound intensity level in...Ch. 17 - (a) What are the loudnesses in phons of sounds...Ch. 17 - Suppose a person has a 50—UB hearing loss at all...Ch. 17 - If a woman needs an amplification of 5.01012 times...Ch. 17 - (a) What is the intensity in watts per meter...Ch. 17 - (a) Find the intensity in watts per meter squared...Ch. 17 - A person has a hearing threshold 10 dB above...Ch. 17 - A child has a hearing loss of 60 dB near 5000 Hz,...Ch. 17 - What is the ratio of intensi?es of two sounds of...Ch. 17 - What is the sound intensity level in decibels of...Ch. 17 - Is 155—dB ultrasound in the range at intensities...Ch. 17 - Find the sound intensity level in decibels of...Ch. 17 - The time delay between transmission and the...Ch. 17 - Prob. 76PECh. 17 - (a) Calculate the minimum frequency of ultrasound...Ch. 17 - (a) Find the size of the smallest detail...Ch. 17 - (a) Echo times are measured by diagnostic...Ch. 17 - (a) How far apart are two layers of tissue that...Ch. 17 - (a) A bat uses ultrasound to find its way among...Ch. 17 - A dolphin is able to tell in the dark that the...Ch. 17 - A diagnostic ultrasound echo is re?ected from...Ch. 17 - Ultrasound reflected from an oncoming bloodstream...Ch. 17 - Prob. 1TPCh. 17 - Prob. 3TPCh. 17 - Prob. 4TPCh. 17 - Prob. 5TPCh. 17 - Prob. 6TPCh. 17 - Prob. 7TPCh. 17 - Prob. 8TPCh. 17 - Prob. 9TPCh. 17 - Prob. 10TPCh. 17 - Prob. 11TPCh. 17 - Prob. 12TPCh. 17 - Prob. 13TPCh. 17 - Prob. 15TPCh. 17 - Prob. 16TPCh. 17 - Prob. 17TPCh. 17 - Prob. 18TPCh. 17 - Prob. 19TPCh. 17 - Prob. 20TPCh. 17 - Prob. 21TPCh. 17 - Prob. 22TP
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