On Sep 12, 2011, at 4:10 PM, Stephen A. Lawrence wrote:
On 11-09-12 05:18 PM, Horace Heffner wrote:
On Sep 12, 2011, at 10:59 AM, Stephen A. Lawrence wrote:
On 11-08-25 10:33 AM, Abd ul-Rahman Lomax wrote:
At 06:55 PM 8/24/2011, Jed Rothwell wrote:
Here is an interesting footnote to history. I believe the speed
of sound was not established with this much precision until
later. This was done by assuming for simplicity that the speed
of light is close to infinite over short distances, and firing
a cannon. The time delay from the flash to the sound of the
explosion gave the speed of sound. This was done in 1826 at
Lake Geneva to establish a value to within 1% of the modern
figure. I don't know how they recorded it. I guess by pressing
buttons to start and stop a timer. You would think this would
mainly record human reaction time but I suppose it depends on
how far away the cannon was.
The reaction time would affect both start and stop timing,
probably about equally. Only if the interval were short such
that variation in reaction time would be a major chunk of it
would reaction time be a serious problem.
Since the human reaction time is added to the clock reading at
both ends, and you're taking the difference, the error it
introduces should be essentially random, due to variation in the
reaction time. And in that case, you can just repeat the test a
dozen times and average the results. Noise which is largely
random will tend to cancel out, leaving you with something very
close to the true "noise-free" result. (That assumes, of course,
that the same person notes both the bang and the flash -- if two
different people record the two events, using two different
nervous systems, you've introduced a possible source of
systematic error!)
Errors in reading a sweep hand should also be random, and hence
should also cancel out when averaged over many trials.
And after that, the biggest source of error may be the accuracy
of the clock itself. Clock technology was driven by the need for
accurate navigation, and was pretty good pretty early. So it
seems reasonable they could have gotten a very good result with
that technique.
The main problem for anyone trying to precisely replicate the
result, of course, will be the limited availability of really
good cannons. (Maybe try Ebay...)
Visible paths over Lake Geneva can be very long, especially if the
observer is on a hill or mountainside, and a telescope is used.
For example, the path between Nyon and Montreux is about 48.6 kM.
Using 340 m/s as an estimated speed of sound, the delay is about
143 seconds. A 1% error thus represents 1.43 seconds. Variations
due to humidity and temperature would be large compared to human
reaction time error.
Indeed!
Wind would play a role too, I suspect.
That's a pretty impressive baseline -- I hadn't realized the
significance of the choice of a location by a lake surrounded by
hills, and it hadn't occurred to me that they'd used a telescope
(which they surely would have done).
Yes, wind is very important - not to the velocity so much as to the
focusing of sound over a flat terrain, so that it can be heard at
great distances. I know from personal experience that a following
wind over flat terrain greatly increases the distance at which things
can be heard. I think the effect is called "SOCUS".
http://www.tpub.com/content/aerographer/14010/css/14010_160.htm
http://tinyurl.com/3jnchdk
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
