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).