Oryoki (and Martyn),
I think you are right regarding finding the focus by testing using
light or sound rather than trusting the original math.
For planning dish design and to create a basic template for the
curvature I might use a basic formula such as the one in the page you
referred to, or here's another useful page I found through Wikipedia:
http://mathworld.wolfram.com/Parabola.html
I might use MS Excel to solve for increments of height(y) or
radius(x), and would play with various distances from the vertex to
focus(a) in the equation until the overall dimensions seemed about right.
Still my primary question remains - where to place the theoretical
focal point as the basis of a dish design?? And should this be a set
distance from the rim =96 1.5 maybe 2 inches, or a ratio of the height
of the dish =96 like 0.6 or 0.9?
Besides standing waves or cavity resonance, and considering a focus
less than the height of the dish to isolate from background noise, the
reason for having the focal point close to the height of the dish
seems for the sake of efficiency of space and materials. The wider
the dish the lower the amplified frequencies =96 right? And for any
given dish width, the shorter the distance from the vertex to the
focus the deeper the dish will be. And the deeper the dish with
respect to the width the more material it would need and the more
cumbersome to handle it would all end up.
Throwing these practicalities aside and considering only acoustical
properties, what would be the ideal shape of a parabolic reflector for
nature recording? I'm imagining an eight-foot dish a couple feet deep
for recording from shore a back set of breakers in a twenty-foot
swell, or maybe a slightly smaller one for recording from the lookout
by the jetty the birds and other activity in the channel near the
Columbia River bar.
-John Hartog
>
> "John Hartog" wrote:
> > Would the optimal position of the focus be at a certain
> > ratio of the dish depth?
>
> I like this approach:
>
> "...Rather than trying to make measurements to determine the equation
> and calculate the focus from those measurements, you'd be better off
> finding the focus directly by experimentation.
>
> [Assuming the parabolic dish has a reflective surface] Shine several
> parallel light beams at the dish, each parallel to the main axis of
> the dish, and observe where they converge.
>
> You'd likely get more accurate results that way than trying to
> determine the equation of the dish by measurements."
>
> http://www.math.toronto.edu/mathnet/questionCorner/parabolic.html
>
> Alternatively, you can simply move the mic in and out on its mount and
> listen to the signal the mic produces to find the spot where you get
> the best results.
>
> --oryoki
>
|