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Given y=Ax^r where A and r are constants, how can you show that it will give a straight line on a log-log graph. Obviously selecting various values for A and r gives you a straight line on a log-log graph but how can you show that in generality?

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Reid Wolff
Reid WolffLv2
17 Aug 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Figure 13.18 shows the periods of planets in our solar systemvs. their orbital radii on a log-log scale. Curiously, the datapoint for the Moon is not in that figure. If we added the Moon tothe graph, where would it be relative to the straight line? Theastronomical data for the Moon are listed in Table 13.2.

Note: for the Moon, the horizontal axis is the distance from earth,not from sun.

A) On the straight line.
B) Above the straight line.
C) Below the straight line.

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B. One can purchase so-called Ceramic speakers which haveavibrating ceramic instead
of a coil-driven cone to produce sound waves. These arecapableof producing
frequencies well above the range of human hearing and, infactare used for sonar and
ultrasound applications. The disks used have aconductivecoating applied to either side
of the disk and the ceramic material reacts to anappliedvoltage by contracting or
expanding by an amount proportional to the voltage.Thesedevices are capacitive rather
than inductive.
1. Write the expression for the impedance of such a speakerinterms of the resistance
and capacitance.

2. Find an expression for the frequency ω at whichtheresistance equals the reactance of
the ceramic speaker, in terms of R and C.

3. With R = 8Ω and C = .25μF, calculate thefrequency ω, withunits, that will give R =
XC .

4. Using ωo for the frequency you calculated in 3,calculatethe total impedance, Z, for
the following frequencies and plot the results on the logplotprovided.

Table
ω/ ωo 10-4 10-3 10-2 10-1 1 10 102 103 104
Xc
Z

6. Locate your answer for part (2) on the plot. What featureofthe plot corresponds to
that answer? [4 points]
7. Describe how to quickly sketch this log-log plot for anRCcircuit with only one
calculation, based on your answer to (6). [5 points]
Impedance
0
1
2
3
4
5
6
7
2 3 4 5 6 7 8 9 10
log(omega)
log(Z)
8. Using the same resistance of 8Ω, what value fortheinductance in an LR circuit would
give XL = 8Ω at the same ωo value calculated in 3?
9. Using ωo for the frequency you calculated in 3,calculatethe total impedance, Z, of the
LR circuit for the following frequencies and plot theresultson the log plot provided.


Table
ω/ ωo 10-4 10-3 10-2 10-1 1 10 102 103 104
XL
Z


Male Rana catesbeiana bullfrogs are known for their loud matingcall.The call is emitted not by the frog's mouth but by itseardrums, which lie on the surface of the head. And, surprisingly,the sound has nothing to do with the frog's inflated throat. If theemitted sound has a frequency
--------------µm
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