How Do Diameter, Focal Length, and Distance Affect Whisper Dish Efficiency?

[jds10011]

TL;DR

We know that satellite and other dishes are parabolic. What factors determine which parabola is used and how well they work?

We're trying to build working models of "whisper dishes" -- two large parabolic dishes placed at a distance and pointed at each other, allowing two people to communicate by whispering at the focal point of one dish and listening at the focal point of the other (or vice versa). At a fairly rudimentary level, we are looking for more information on how well this setup will work based on (a) the diameter of the dish (b) the focal length of the dish (c) how much of the parabola is present, if not already accounted for in (a) and (b), and (d) how far apart the dishes are placed. Can you point us in the right direction of better understanding? At the very least, what is likely to be a "good" shape/size for our model (what equation would we use and what diameter, along with what distance)? (And, yes, we're aware that the dish needs to be large enough that the speaker's/listener's head isn't blocking the "signal".)

Also, we are curious if the answer would be different for other applications, such as a dish for satellite tv, or the classic parabolic reflector dish used for frying eggs on a sunny day.

Lastly, we are wondering how much tolerance there is in these setups -- for example, if the aim is slightly imprecise, if the speaker/listener is slightly off from the focal point, if the shape of the parabola is slightly imprecise in the construction of the model, etc. -- at the very least, what are major and minor sources of error?

 

[Baluncore]

Experiment with a couple of used satellite dishes, if you can find them.

The beam between the two dishes is roughly parallel, so the distance between dishes is not a big problem.

For voice, a dish with a diameter of between 1 and 2 metres is OK. The focal length should be similar, with the dish depth about half that, so the person speaking and listening, is outside the dish, while most of the voice will "illuminate" the dish surface. The head of the operator should be at the focus, so different people need to stand or sit at different heights, without needing a stepladder.

Surface accuracy should be ± λ / 20 at the highest frequency.
For 3 kHz audio, λ = 343 / 3kHz = 115 mm.
The surface accuracy should be better than; 115 / 5 = ±6mm.
Holes in the surface must be smaller than λ / 10 = 12 mm.


The dish profile can be shaped by rotating a profile pattern in a sandpit, then the dish can be cast from concrete, and used as part of a garden wall.

For a flattish dish, a shallow spherical surface may be close enough.
If you need more room, you can use a flat wall as a plane reflector along the path.

You may get away with the top half of the dish only, if you have only one, and cut it in two. The bottom half of the dishes are partly obstructed by the body of the operator, and other obstructions or people in the area.

https://en.wikipedia.org/wiki/Acoustic_mirror

 

[sophiecentaur]

Surface accuracy should be ± λ / 20 at the highest frequency.

That's a fair rule of thumb for an ideal source / detector (tiny microphone) at the focus. But a head (plus two ears) will be about 200+mm so the focused sound image needs to be no better than that. So I doubt that performance would suffer with a spherical profile.

The dish profile can be shaped by rotating a profile pattern in a sandpit, then the dish can be cast from concrete, and used as part of a garden wall.

A good, cheap solution, if it doesn't need to be pointable. If you don't mind the smell then fibreglass is light and fairly cheap. For indoors, papier maché is even cheaper and easy to fabricate.

I like the idea of using less than a full hemisphere. Much easier to mount and rotate.

 

[A.T.]

... and used as part of a garden wall.

Always good to know what the neighbors are up to

 

[Baluncore]

Always good to know what the neighbors are up to

The advantage of an offset-fed dish, with a microphone at the focus, is that your neighbours do not know you are listening.