[Phys-L] Light bulbs and Nyquist's Theorem

[John SOHL <jsohl@WEBER.EDU>]

Michael has some excellent results. Actually, they don't differ by that
much from mine. What you can see in mine is a beautiful example of
flawed experimental data. As I had alluded to in my earlier message I
was limited by the speed of my system. Actually, the speed limit it
turns out was not my computer but the USB port. The standard
round-trip
polling time of a USB port is 20 ms according to the data acquisition
board's manual. I was able to get it to do 16 ms at best and that was
not uniform. I could easily get 20 ms at uniform pacing.

My result showing the 5-Hz behavior that Michael points out is exactly
what one would expect from combining a 60 Hz signal (actually 120 Hz)
with a 50 Hz data collection rate. It is the same problem that causes
wagon wheels to do "funny" things in western movies. When the frame
rate
of the camera is not significantly higher (at least 2 times) then one
over the time needed for one spoke to move to the position of the next
spoke then you get the odd appearance of the wheels moving slowly or
backwards. Much like watching things with a strobe light when the
frequency of flashing is a bit off from the frequency of the item
under
observation.

In sampling theory this is known as Nyquist's Theorem. To obtain a
reading with the minimum number of data points and still obtain a
correct value for the frequency you must sample at a rate of at least
twice the expected frequency of the phenomena that you are measuring.

Thus, for this measurement we need to sample at a rate of at least 240
Hz. Michael's oscilloscope was easily doing this. In my case, I needed
to get some programing done anyway for a simple data acquisition
system
in my optics lab, so I used this as an excuse to get it done. It also
gives me more flexibility then using a scope but much less resolution.
I
have used the scope to observe many light sources over the years and
have always been tickled that you can see the 120 Hz in an
incandescent
lamp so I expected that part.

In reading the manual for the data acquisition board I have an idea
that might beat the speed of the USB. While I have computers with fast
internal PCI cards for data collection, I need to get this system in
the
optics lab up and running anyway. I now think that I might be able to
sample at a rate of 1.2 kS/s. That would give me the needed speed and
a
sample rate of 10 samples per period which is about perfect. I'll let
you know what happens. (The photodiode system is not causing any
timing
issues here, it should work well to at least 200 kHz. Using a pulsed
laser with 500 ps pulses I have measured a rise time of about 30 ns
with
this system but the op amp is not able to slew fast enough to maintain
good gain at that speed.)

On other notes:
1. I considered doing DC turn on/off but that is not what the
"man-on-the-street" is observing so I specifically decided not to do
it
that way.

2. I'll happily measure bc's 6V lamps. Drop one or two in the mail
(address below) and I'll run them. The current rating shouldn't
matter,
I'll put the specified voltage across them and see what happens. I
have
a programable DC power supply that can supply up to 50 volts at 100
amps
with rapid turn on/off of the power. That should be well more than
enough for most small lamps. Let me know if you want me to send them
back when I'm done.

3. I did watch my lamps over extended periods of time and they did not
change significantly in brightness. I also waited between turn ons to
allow the bulb to cool and that didn't make any significant difference
either. There were a couple of times that I did see a longer period
drift in the output but I think the system might have moved a bit
causing the distance between the bulb and photodiode to shift.

4. A series circuit of bulbs of various wattage is a fun demo for
physics classes but not good for the issue at hand. These bulbs were
not
designed to run in series that way and so you are testing them in a
fashion that no typical person would ever observe. Asking if a light
flares in brightness upon turn on then measuring a different system
doesn't answer the original question posed by John D.

In the end, the observed "flare up" of the bulb upon turn on is not
caused by the bulb but by the automatic brightness adjustment feature
of
the human eye and most video cameras. I even noticed it with the
bright
LED that I used in my test and I'm sure there is no error in my
measurements of that.

Since childhood I have noticed that bright incandescent lamps take a
second or so to completely turn off. As a result of these tests, I now
believe that is caused by the persistence of vision (a combination of
saturation of the eye's sensors and the eye's frame rate). But, I'm
going to make some measurements of bright bulbs anyway.

John

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
John E. Sohl, Ph.D.
Professor of Physics
Weber State University
2508 University Circle
Ogden, UT 84408-2508

voice: (801) 626-7907, fax: (801) 626-7445
e-mail: jsohl@weber.edu
web: http://physics.weber.edu/sohl/

> > > Michael Edmiston <edmiston@BLUFFTON.EDU> 11/14/2005 8:41:25 pm >>>
John Sohl made some measurements and posted them on a web page.  I
have
done the same.  My results can be found at

www.bluffton.edu/~edmistonm/light.bulb.pdf

My results are similar to John's but different.

(1) I don't understand the oscillations in John's plots.  If the time
scales are correct, the oscillation period is about 200 ms giving a
frequency of about 5 Hz.  This might seem to be a vibrating filament
except John's fluorescent bulb also showed the 5-Hz behavior.  That
makes me think his time scale is incorrect.

My filament clealry showed 120-Hz oscillations in light output caused
by
the 60-Hz AC power.  The magnitude of these oscillations is
considerably
more than I would have guessed.  I wasn't sure they would be visible
at
all, but they amounted to about 18% of the average light output.
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