What is Isotropic: Definition and 122 Discussions

Isotropy is uniformity in all orientations; it is derived from the Greek isos (ἴσος, "equal") and tropos (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

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  1. T

    Deriving the line element in homogenous isotropic space

    If the Ricci-scalar R is constant for a given spatial hypersurface, then the curvature of that region should be homogenous and isotropic, right? A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry): d\sigma^2 =...
  2. S

    Energy-mom tensor of charged dust (homogeneous and isotropic)

    You have charged dust (pressure = 0, charge density/mass density = given constant). I suppose the total energy-momentum tensor of that system (including the rest energy and the EM field) cannot be expressed simply in terms of the arbitrary 4-velocity of the dust like for example the case of...
  3. F

    How can you tell if the interaction is isotropic?

    Homework Statement A teenager has a car that accelerates at 3.00 m/s2 and decelerates at -4.50 m/s2. On a trip to the store, he accelerates from rest to 16.5 m/s, drives at a constant speed for 5.00 s, and then comes to a momentary stop at the corner. He then accelerates to 18.0 m/s, drives at...
  4. J

    Calculating Sound Energy from Isotropic Loudspeaker

    1. Homework Statement The sound level 24 m from a loudspeaker is 66 dB. What is the rate at which sound energy is produced by the loudspeaker, assuming it to be an isotropic source? ____W 2. Homework Equations ? Something to do with Intensity? 3. The Attempt at a Solution...
  5. C

    What Does Isotropy Mean in a Two-Dimensional Harmonic Oscillator?

    Find the find the eigenfunctions and eigenvalues of a two-dimensional isotropic harmonic oscillator. I don't understand what does isotropic here mean. isotropic can be defined "not changing" when the coordinate change to any other position. Am I correct? Like mass, pressure...
  6. N

    Homogeneous and Isotropic Stress-Energy Tensor in Cosmology

    This is a very basic question but what is the difference between isotropic and homogeneous? I mean, I can imagine a universe that would be isotropic but not homogeneous although this seems to select a preferred frame (am I worng on this?) But I don't understand how it would be possible to have a...
  7. B

    Isotropic 3-D harmonic oscillator

    Homework Statement Use Frobenius’ method to solve the problem of the isotropic three dimensional harmonic oscillator in polar coordinates. It is sufficient to find the energy levels and degeneracies, but it would be nice to plot the spectrum like we did for hydrogen. Be sure to introduce...
  8. S

    Isotropic Radiation Propagation Patterns

    Hello, I'm trying to plot a radio wave propagation plot of an isotropic antenna. I've found a collection of equations that I've tried to use, but the results that I'm getting, aren't exactly what I expect (not a circle or sphere, since the power is equally distributed). Here is the...
  9. D

    Poisson's Ratio and Ultrasonic Velocity for Isotropic Material

    For an isotropic material, the relation between the longitudinal ultrasonic velocity(VL), the transverse (shear) ultrasonic velocity(VT) and the Poisson's ratio (nu) is given by (VT/VL)^2 = (1-2*nu)/(2*(1-nu)) From the above relation, one gets that VL=0 when nu=1 which is not...
  10. S

    Isotropic loudspeaker - calc based

    1) Isotropic loudspeaker A certain loudspeaker system emits sound isotropically with a frequency of 2.00 x 103 Hz and an intensity of 1.00 x 10-3 W/m2 at a distance of 7.00 m. Assume there are no reflections. Use 344 m/s for the velocity of sound in air and 1.21 kg/m3 for the density of air...
  11. A

    Why Do Some Tensor Functions Appear Isotropic in Component Notation?

    Hello, I consider only Cartesian tensors in the following. The definition of isotropic tensor function I know is 1) T = F ( G ) such that, for any rotation ( ' = transpose), 2) O F( G ) O' = F( O G O' ) But, if I change to component notation, it seem to me that any tensor function is...
  12. P

    Difference between spatially homogeneous and isotropic?

    What are their differences? Spatially homogeneous is when there is uniform composition of space Spatially isotropic is when you look anywhere, they look the same Is it the case that one is visit anywhere, it is the same and the other is look anywhere they look the same? They seem...
  13. Amith2006

    Luminous intensity due to an isotropic point source of light

    Does the luminous intensity due to an isotropic point source of light at a point on a surface depend on the angle it makes with the normal to the surface?
  14. S

    Analytical mechanics: 2D isotropic harmonic oscillator

    I'm stuck on this problem: The initial conditions for a two-dimensional isotropic oscillator are as follows: t=0, x=A, y=4A, v=0i +3wAj (vector) where w is the angular frequency. Find x and y as functions of t. Where do I even begin with this problem. I take it A = constant. Can anyone...
  15. E

    Shifting the origine of time in isotropic oscillator

    I am really lost here :( The equation of motion X(t)=Ax Cos(wt-delta(x)) Y(t)=Ay Cos(wt-delta(y)) by shifting the origine of time ( t'=t+to where I need to figure out what is appropriate for time to ) and ( Delta=Delta(y)-Delta(x) ) I am suposed...
  16. B

    Isotropic and anisotropic propagation of light

    Do you aggree that there is an inertial reference frame in which light in free space propagates isotropically whereas in all other inertial reference frames its propagation is anisotropic?
  17. S

    Confinement of Motion in a 2D Isotropic Oscillator

    I'm given some initial conditions for a 2-d isotropic oscillator: At t=0: x=A, y=4A, dx/dt = 0, dy/dt = 3wA Solving the differential equations of motion and using those conditions, I get the following: let\ \gamma = tan^{-1}(-3/4) x(t) = A cos(\omega t) y(t) = 5A cos(\omega t + \gamma)...
  18. M

    Understand Isotropic Tensors for Physics

    Hello everyone, this seems like a great forum here with a lot of knowlegable people and I was hoping someone could help me out with this question. I'm an engineering student and I've recently decided to switch into physics. Now I'm trying to catch up on the math I'm going to need, so I'm...
  19. E

    How Do You Solve the 3D Non-Isotropic Oscillator Numerically?

    ok. mass held by six springs and is located at the origin. Potential function is given by V = k/2 (x^2 + 4y^2 + 9z^2). at t = 0 the mass is given a push in the (1,1,1) direction imparting vo. find x(t) y(t) z(t) numerically if k = m(pi^2). part b: will it every get back to origin, if so what t...
  20. E

    What is a isotropic harmonic potential?

    Well, what is it? If two particles are interacting in an isotropic harmonic potential, then how does this differ from an ordinary harmonic potential?
  21. M

    Solving an Isotropic Harmonic Oscillator with Four Identical Springs

    hi, I was going through my homework and i came to a problem that i can't seem to get. Consider the mass attached to four identical spring. Each spring has the force constant k and unstreched length L_0, and the length of each spring when the mass is at the origin is a(not necessarily the same...
  22. Antonio Lao

    Is Cosmos Homogeneous, Isotropic ?

    Is Cosmos Homogeneous, Isotropic ? Is the universe really homogeneous and isotropic? The answer is hidden within the structure of spacetime.
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