1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Amplitude decrease with geometrical spreading

  1. Aug 1, 2014 #1

    I'm looking at amplitude decrease of a seismic pulse as a result of geometrical spreading.

    Starting with I = E / (4 * pi * r2) where E = original energy from source, we know that energy falls off as 1/r2, thus amplitude falls off as 1/r.

    From wikipedia: "The energy or intensity decreases (divided by 4) as the distance r is doubled;"

    This makes sense to me, as when r is doubled we have the energy divided by (2r)2 = 4r2 (which is 4x r2).

    From this same principle, I would expect that the amplitude is divided by 2 when the distance is doubled as we have 1/2r instead of 1/r.

    However from a Louisiana State University website:

    "Geomteric spreading makes the amplitude of a signal falls off in proportion to the distance traveled by the ray. So that if the path of flight is doubled the amplitude will decrease by a factor of: square root of 2."

    I can't see how they got their factor of √2 instead of 2.

    Is one a mistake or am I missing something?

  2. jcsd
  3. Aug 3, 2014 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Think of a compression/sound wave spreading out from a source equally in all directions as concentric spherical shells of energy. The energy in a given shell is constant. So the energy density is inversely proportional to the area of that sphere: i.e. energy per unit area varies as 1/r^2 where r is the radius of the shell.

    The question you are asking has to do with the relationship between amplitude and energy density of a wave front. Think of the vibration of a spring: the energy contained in the spring is proportional to the square of the maximum amplitude. PE = kx^2/2 .

    Since the energy contained in the wave front is proportional to the square of the amplitude and the energy density is inversely proportional to r^2, how would amplitude vary with r?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook