It is rather a late reaction, but I thought you might enjoy the following observations:
Echoes by stairs "I would like add to this a rather remarkable observation that I did when I was at Chantilly de la Cour, by the equestrian statue. A stair of ... steps descends into the garden, where a fountain continually murmurs.When at the bottom one places oneself between the stair and the fountain, one hears from the direction of the stair a resonance that has a certain musical sound to it, and that continues for as long as the fountain works. Locals did not know whence this tone came or produced improbable explications for it, so that I wanted to find a better one. I soon found that the tone was caused by the reflection of the fountain's murmur by the steps of the stair. For any sound, or rather any noise, that is repeated with equal, small interstices, gives a musical tone..." Christian Huygens (Oeuvres Complètes, 10, 570), 1693. Whistling echoes "An observer is unconsciously always hearing the sound of his footsteps, which is different according to the nature of the road and its surroundings. Especially at night, when all is quiet, we notice sometimes how that sound may suddenly become quite peculiar, almost metallic: each step sounds like "tyiuuu". It always turns out that a fence is beside the road, and on further investigation this proves to be the cause of the whistling echo. The fence should be at least four meters, the distance between the rods too small nor too large. Explanation: the sound of the step in S is reflected in turn by rods A, B, C, ... , L, M, N, ... (or rather diffracted, Huygen's principle!). The weak echoes reach our ear not at the same time, but one by one, because SAS, SBS, ... , SLS, SMS, .. are gradually longer. The triangles LPM, SAM are similar, so the difference for two rods 2PM = 2LM sin alpha, and the frequency of the reflected sound is 340 / 2LMsin alpha. At every step first the closest, then the more remote rods are involved; sin alpha is first zero, increases and approaches 1. One hears, then, a very high pitch, that soon becomes lower and approaches a fixed limit. If the rods are, for example, 17 cm apart, the frequency of this "final pitch" is 1000 Hz, still rather high. This is in fact what one hears, but the rapid pitch change does not admit of an accurate estimate of pitch... " Dr. M. Minnaert (of "Light and Colour" fame), 1943. ----- Original Message ----- From: John Carmichael <[EMAIL PROTECTED]> To: Roger Bailey <[EMAIL PROTECTED]> Cc: <[email protected]> Sent: Tuesday, March 21, 2000 4:03 PM Subject: Chichen Itza echo effect > Hi Roger: > > I've enjoyed your postings about Chichen Itza as it is my favorite pyramid > in Mexico. Here are a couple of unrelated tidbits that I thought might > interest you. > > When I visited the Chichen Itza pyramid years ago, I noticed that that if I > stood in front of the "good " side (not the side that is still in ruins) and > clapped my hands, the most curious echo I've ever heard resulted that > sounded like "zzzzzing". Even the guide didn't know about the echo effect. > Later in the day of my visit I saw a bunch of tourists clapping their hand > imitating the guide! > > Also, I love building sand castles when at the beach, and the Chichen Itza > pyramid is one of my favorites things to build as it is fairly easy to do > and very erosion stable. > > Take care, and enjoy your warming temperatures! > > John Attachment converted: Macintosh HD:fluiten.gif (GIFf/JVWR) (0001B69C)
