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  1. R

    I How would one calculate the distance and bearing of a signal source?

    That's the standard approach. But if you are able to determine the distance to multiple receive points based on power measurements, you can geolocate the source that way as well.
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    I How would one calculate the distance and bearing of a signal source?

    That's not true at all! If we have an angle less than 45 degrees, then the opposite of that angle will be the shortest side. Since that angle can be anything in the range ##0^\circ < \theta < 45^\circ##, the ratio opposite/hypotenuse ##= \sin(\theta)## can be anything in the range ##0 <...
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    B Question about expanding a function to first order

    You can answer this yourself. Draw a curve, any curve. That's ##f(x)##. Draw the tangent line at any point ##x_0##. That's the line ##f(x_0) + f'(x_0) \Delta x##. How far is the line from the curve? Anywhere it's "close enough", whatever that means to you, is a place where the approximation is...
  4. R

    Optimization of objective function that's the product of unitary matrices

    What is constant and what is a variable here?
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    B Convention when changing integral limits

    Yeah, that's definitely wrong. The author fixes things by changing variables at (2.1.16) so that the limits now make sense but the equations before that point are nonsense. The ##v## is just serving the role of placeholder in (2.1.13-15), "this equation is incorrect and something else goes into...
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    Question for people who have traveled to Italy

    I've been to Italy several times but have never used a car so I can't comment on that. It was precisely because of worries about dealing with traffic, aggressive drivers and finding parking that we have always opted to get around by train. You are correct that this limits your ability to visit...
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    I Rudin: theorem 1.21

    Because ##x## is positive, so (x + 1) > 1, so ##x/(x+1) < x##. Style note: ##X## and ##x## are different symbols. You should stick to one or the other and not treat them as interchangeable.
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    B Why does a capacitor charge to 63% of the applied voltage?

    Late to the thread, but my $0.02 worth: The differential equation people are referring to is the physics equation that describes how fast the capacitor charges at any given instant, and it's related to how much charge is currently on the capacitor. The principle that the capacitor "knows" is how...
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    Acceleration graph

    Let me talk a little in general about velocity and acceleration and what direction changes are in. You know that ##a = \Delta v/\Delta t##. If ##\Delta v## is positive that means ##v## increased. An increase could be going from 0 to 3, or from 2 to 5, or from -1 to +1, or from -5 to -2. [No...
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    I Fast Fourier Transform in MATLAB

    A digital Fourier transform (DFT) is a transformation of n points. The equations are a sum from 1 to ##n##. ##n## is the number of points you are transforming. The number of time values. And you will get out the same number of frequency values. If you do a 32-point transform, transforming 32...
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    Algebraic manipulation with factorials

    Wait, you're saying that the ##(n+1)##-th term is found by adding 1 to the ##n##-th term? Are you sure about that? You might want to check a few terms. Evaluate ##a_1##, ##a_2## and ##a_3## and see if you think that's still true.
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    I How electrons absorb or emit photons

    Both. I'm not sure why you the fact that an electron absorbs a photon contradicts the fact that an electron can emit a photon. Perhaps it's the phrase the photon that is your problem. The original photon is gone. If the electron goes back to the ground state, a new photon is created with the...
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    Need a cancer to fit a fictional plot

    Thank you and I apologize for hitting too close to a painful reality. I'm not planning on treating it lightly.
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    Need a cancer to fit a fictional plot

    Summary: For fictional purposes, looking for a cancer which has a very low survival rate but which a patient might be fighting for 1-2 years I'm sure that this is actually a fairly common sub-genre of medical questions, authors asking for a disease to fit a story. I have a lot of side...
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    MATLAB Approximating the inverse FT of a unit pulse using a Riemann sum

    I should have caught that as I have extensive experience with Matlab and I'm well aware that zeros(50) means a 50x50 matrix. But my normal approach to debugging is to set a breakpoint, then try to build the problem expression bit by bit and see where it fails, and then use that as a clue to what...
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    Electric field due to two positive charges

    In the lecture, he is calculating the field of a dipole where one charge is positive and one is negative. The y-components cancel out and the x-components add. That's not the case here. Draw the vectors representing the fields from those two identical positive charges. They do not cancel out in...
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    MATLAB Approximating the inverse FT of a unit pulse using a Riemann sum

    Do you have any experience in debugging Matlab? It's hard to diagnose this from looking at the code. Add the command "dbstop if error" after line 4, since your "clear all" clears all breakpoints and they need to be reset. If you get the error, check the different parts of that assignment, such...
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    I Fourier series representation

    Here is a simpler example of what's happening here. Define ##g(\alpha) = \int_1^2 (\alpha t)^2 dt##. That may look like a function of ##t## to you, but it's not. ##t## is a dummy variable which does not exist outside the integral sign. We can explicitly calculate the value of ##g(\alpha)## by...
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    I Fourier series representation

    Which is independent of ##\alpha##, and therefore is unaffected when you change ##\alpha## to ##-\alpha##. When you make that change, the equation for ##g(\alpha)## is completely unchanged and therefore results in exactly the same function. The question of whether ##g(\alpha)## is even is in...
  20. R

    Science-related tourism in Paris

    Hi all, just thought I'd update this thread with what I actually ended up doing. My hotel for the weekend was in the Montparnasse neighborhood, for no particular reason except that it came up as a reasonably-priced, reasonably-central hotel in my search. I found a bookshop and purchased a book...
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    Seemingly simple Physics 2 wave question (third harmonic frequency)

    1. For what values of the argument ##\theta## does ##\sin(\theta)## equal 1/2? 35 cm corresponds to ##kx## having that value. Since you know what ##x## is, that gives you possible values for ##k = 2\pi/\lambda## and therefore you can work out ##\lambda##. 2. For the third harmonic, what is the...
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    I Fourier series representation

    The author says the integrand is an even function of ##\alpha##, so ##\int_{-\infty}^0 d\alpha## should be the same as ##\int_{0}^{\infty} d\alpha##. You have a sign error in your third line. Let's define ##g(\alpha) = \int_{-\infty}^{\infty} f(t) \cos \alpha(t - x) dt##. Then ##g(-\alpha) =...
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    I Fourier series representation

    I can see why you prefer the trigonometric form and are a little distrustful of the complex form. These are representations of real signals. As such, they only have positive frequencies, and their value better turn out to be real. The exponential form is much easier to deal with mathematically...
  24. R

    I What is the proof of the rules of significant figures?

    Let's say for instance you have a measured value which you write as ##x = 2.3##. What that is supposed to mean is that you're confident of the 2 and the 3, but not of any further figures. You don't mean that the real value is 2.3000. You mean it's approximately 2.3. You mean that it could be...
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    I Fourier series representation

    That's incorrect. Having only one frequency at baseband doesn't mean you'll have only one frequency after mixing up. Let's analyze a simple amplitude modulated carrier wave. Let's say the carrier frequency is ##\Omega## (I'm going to use angular frequencies such as ##\Omega = 2\pi F## to avoid...
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    Is there anything wrong in this question statement?

    As @DaveE says, it depends on what type of model you're studying and supposed to be applying. A more common model for growth is exponential, ##P = P_0 e^{at}## or ##P/P_0 = e^{at}## in which case you're expected to use the given value of ##P/P_0## first to solve for the rate constant ##a##.
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    MATLAB Plotting standard deviation in Matlab

    It sounds like you want the ERRORBAR function. https://www.mathworks.com/help/matlab/ref/errorbar.html
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    A The partial derivative of a function that includes step functions

    S is a function which takes on discrete values, and jumps instantaneously between those values. The time derivative is either 0 (between jumps) or doesn't exist (at jumps). Yes, in physics we do that. It's not exactly rigorous but makes a certain kind of sense. The Heaviside function has a...
  29. R

    What avenue of physics can a scientist in the Star Wars galaxy study?

    They could work on more accurate weapons for Stormtroopers. Also armor that can't be defeated by rock-wielding Ewoks.
  30. R

    I Ambiguous Results for two Fourier transform techniques

    So let's check. You have ##F(\alpha) = \frac {\alpha} {b + i\alpha}##. So that gives ##F(-\alpha) + F(\alpha)## = ##\left ( \frac {-\alpha} {b - i\alpha} \right ) + \left ( \frac {\alpha} {b + i\alpha} \right )## = ##\frac {-\alpha(b + i\alpha) + \alpha(b - i\alpha)} {b^2 + \alpha^2}## = ##\frac...
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