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Short version: If an omnidirectional signal is being sent from one side of an object that causes appreciable attenuation does it result in an egg shaped detection envelop or something stranger?

Long version: As I understand it a point source omnidirectional signal should emanate equally in all directions and thus, in a perfect vacuum, should be detectable in a spherical volume dictated by the initial signal strength. However many of the source points for signals are not free floating antenna, they're mounted on ships, or stations, or even planet based. I was thinking about how signal detectability changes when the source is mounted on an object or structure that blocks an appreciable percentage of the initial output across half the theoretical sphere. Can we model the shape of the dectability envelope thus formed and what is that shape?

My immediate thought was something egg-shaped but then I couldn't work out what way around it would face viv-a-vis the occluded side and where the source would sit within it etc... and thought possibly the shape is far less straight forward.

For the purposes of answering this query please consider a case where the source is effectively sitting on a flat plate that absorbs half the initial signal strength that would other wise travel in that direction, on other side the signal is unimpeded and the signal is remains detectable down to, but not below, 1% of initial strength.

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    $\begingroup$ In the real world there are few infinitely large infinitely thin obstacles, and the propagation would depend of the relationship between the wavelength of the signal and the size and shape of the obstacle. For example, for a 5 GHz 802.11ac WiFi signal an ordinary buiding will create a shadow, whereas a 200 kHz longwave radio signal will go around even a medium sized mountain. $\endgroup$
    – AlexP
    Dec 24 '21 at 9:24
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    $\begingroup$ In short... it's complicated. $\endgroup$ Dec 24 '21 at 9:31
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    $\begingroup$ It looks like it is better suited for physics stack than here. $\endgroup$
    – Mołot
    Dec 24 '21 at 12:13
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    $\begingroup$ I've voted to close, but I'd like to see it migrated in preference. It's worth looking into antennas - dipoles and arrays and whatnot to get an idea of what the available types are and what they do, including genetic-designs. $\endgroup$ Dec 24 '21 at 15:04
  • $\begingroup$ @AlexP Ah I knew I'd overlooked something, I wasn't intending to posit an infinite plate rather something not much larger than the transmitter itself. In particular I was thinking about a microwave transmitter beacon on the outer surface of the radiation shielding for a starship or space station but looks like I might do better elsewhere. $\endgroup$
    – Ash
    Dec 25 '21 at 9:32
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the source is effectively sitting on a flat plate that absorbs half the initial signal strength that would other wise travel in that direction, on other side the signal is unimpeded and the signal is remains detectable down to, but not below, 1% of initial strength.

The signal starts with initial power $P_0$, on one half of the space it attenuates until it reaches $0.01P_0$, while on the other half of the space it is first halved and then propagates while being attenuated, again until reaching $0.01P_0$

If the dampening is homogeneous you end up with two joined semi-spheres: the larger one on the unimpeded side, which extends up to the distance where the signal is damped to $0.01P_0$, while the smaller one is again at the distance at which half initial power is damped to $0.01P_0$.

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    $\begingroup$ The radius of larger hemisphere is 41% larger than the radius of the smaller; or, conversely, the radius of the smaller hemisphere is 71% of the larger. $\endgroup$
    – AlexP
    Dec 24 '21 at 9:18

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