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Topic: Hearing the shape of a drum

	YourArt.com >> Encyclopedia >> drum (Site not responding. Last check: 2007-11-05)
		Drums consist of at least one membrane, called a "drumhead" or "drumskin", that is stretched over a shell and struck, either directly with parts of a player's body, or with some sort of implement such as a drumstick, to produce sound.
		On modern band and orchestral drums, the drumhead is affixed to a hoop (also called a "rim"), which in turn is held onto the shell by a "counterhoop", which is then held by means of a number of tuning screws called "tension rods" (also known as lugs) placed regularly around the circumference.
		The sound of a drum depends on several variables, including shape, size and thickness of its shell, materials from which the shell was made, type of drumhead used and tension applied to it, position of the drum, location, and a manner in which it is struck.
	www.yourart.com /research/encyclopedia.cgi?subject=/drum (690 words)

	Drum - Biocrawler (Site not responding. Last check: 2007-11-05)
		Template:Spoken Biocrawler A drum is a percussion musical instrument, consisting of a membrane called a drumhead that is stretched taut over a cylindrical tube that is open at the other end.
		The membrane is struck, either with the hand or with a drumstick, and the tube forms a resonating chamber for the resulting sound.
		In the past, drums were used as a means of communication - see drum (communication).
	www.biocrawler.com /encyclopedia/Drum (295 words)

	Drum - Wikipedia Light! (Site not responding. Last check: 2007-11-05)
		Drums with cylindrical shells can be open at one end (as in the timbales) or can have two drum heads.
		Drums with two heads covering both ends of a tubular shell often have a small hole halfway between the two drumheads; the shell forms a resonating chamber for the resulting sound.
		The sound of a drum depends on several variables including shell shape, size, thickness of shell, materials of the shell, type of drumhead, tension of the drumhead, position of the drum, location, and how it is struck.
	godseye.com /wiki/index.php?title=Drums (609 words)

	Drum, Fresh- water
		The common drum, Pogonias cromis, reaches a weight of 146 pounds and may be recognized by its smoky fl or gray stripes and the double row of hairlike barbells beneath the chin.
		The croakers, drums, sea trouts and other fishes of the family Sciaenidae are well known for their ability to produce a loud croaking or drumming sound, either in or out of the water.
		Although red drum supposedly reach a length of 5 feet, and a weight of 83 pounds, it is probable that such large fish are few indeed.
	www.rsmas.miami.edu /support/lib/seas/seasQA/QAs/d/drum.html (4953 words)

	Drums FAQ
		The Quinto drum is (11") in diameter, the Conga drum is (11 ¾"), and the Tumba-or Tumbadora is (12 ½").
		It is commonly referred to as 'kick drum' or simply 'kick', especially in the rec.pro.audio arena, so as not to confuse it with bass guitar during mixing, recording, etc. They are usually played using a pedal, and are set on their side on the floor.
		In short, drum muffling is affixing some material or substance to the shell or head of a drum, with the result being a change in the drum's duration, timbre, and/or volume.
	www.chrisbsmusic.com /drumsfaq.html (13955 words)

	Spaun Drums -- Recommendations and Resources (Site not responding. Last check: 2007-11-05)
		The drum can be sounded by hitting it with a drum stick or by using brushes, which produce a softer-sounding vibration from the wires.
		In a drum kit, the bass drum is much smaller, most commonly 20" or 22" but sizes from 18" to 24" are quite normal, 26" is not unusual in a big band, and extremes both larger and smaller are sometimes seen.
		Originally two identically tuned bass drums were used for this, but a double beater (twin-pedal) on the same drum using an extension mechanism (see illustration) is now more common, although in a live show nearly all metal bands use two bass drums, as the effect is much more impressive.
	www.becomingapediatrician.com /health/140/spaun-drums.html (1551 words)

	Discover the Wisdom of Mankind on drums (Site not responding. Last check: 2007-11-05)
		Drums with cylindrical shells can be open at one end (as in the timbales) or, more commonly in the Western tradition, they can have another drum head.
		It is usual for a drum to have some sort of hole in to let air move through the drum when it is struck.
		Drums are also played by percussionist's who skills can be called for in all areas of music from Classical to Heavy Rock and all areas in between.
	www.blinkbits.com /blinks/drums (865 words)

	Ivars Peterson's MathLand: Drums that sound alike
		Physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normal-mode vibrations.
		Previously, mathematicians had established that both the area of a drum's membrane and the length of its rim leave a distinctive imprint on a drum's spectrum of normal modes.
		To test the drum theorem, the researchers constructed two cavities corresponding to one of the pairs of shapes discovered by Gordon and her colleagues.
	www.maa.org /mathland/mathland_4_14.html (889 words)

	The Ultimate Drum - American History Information Guide and Reference (Site not responding. Last check: 2007-11-05)
		A drum is a percussion musical instrument, consisting of a membrane called a drumhead that is usually stretched taut over a cylindrical tube that is open at the other end.
		The membrane is struck, either with the hand or some other object like a drumstick, and the tube forms a resonating chamber for the resulting sound.
		A drummer is a person who plays the drums.
	www.historymania.com /american_history/Drum (210 words)

	Hearing
		The mechanics of hearing are straightforward and well understood, but the action of the brain in interpreting sounds is still a matter of dispute among researchers.
		At the low end of the frequency range of hearing, the ear becomes less sensitive to soft sounds, although the pain threshold as well as judgments of relatively loud sounds are not affected much.
		The elongated shape of the lobe causes the notch frequency to vary with the vertical angle of incidence, and we can interpret that effect as height.
	arts.ucsc.edu /EMS/Music/tech_background/TE-03/teces_03.html (2111 words)

	Motorcycles -- Noise and Hearing Loss (Site not responding. Last check: 2007-11-05)
		The hearing process goes through four different modes of energy transmission: acoustic (sound waves in air); mechanical (eardrum and bones); hydraulic (fluid filled inner ear) and electrical (the nerve firing to the brain).
		Modern hearing aids have changed physically over the ears from a fl box that fits in your pocket to a miniature device that fits inside the ear canal.
		D's hearing loss deepens over a period of ears and shows the loss shifting to the left (speech discrimination score of 60 percent).
	hope4hearing.org /motorcycle.htm (1694 words)

	Wikinfo \| Drum (Site not responding. Last check: 2007-11-05)
		A drum is a musical percussion instrument, consisting of a membrane which is usually stretched taut over a cylindrical tube that is open at the other end.
		The membrane is struck, either with the hand or some other object, and the tube forms a resonating chamber for the resulting sound.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Drum (178 words)

	Discworld Chronicle Online Issue 2: Drum mathematics (Site not responding. Last check: 2007-11-05)
		In a maths lecture recently, I was told about a problem put forward in the 1930s, nicknamed "Hearing the shape of a drum" which seemed highly appropriate.
		If you define everything about a drum - surface area, tension and so on - in terms of a matrix M, you can use the equation Mx=kx to find k, a family of solutions which are the frequencies which the drum will produce.
		Two drums, which are identical except for the shape, will sound exactly alike.
	www.derek.moody.clara.net /chronicle/issue2/mathmonks.html (249 words)

	Abstract (Site not responding. Last check: 2007-11-05)
		NMR microscopy measures the time decay of the intensity of magnetic radiation of polarized excited dipoles in a given region (e.g., in a biological cell).
		The problem of ``hearing the shape of a drum'' is to recover the shape of a drum membrane from the sound it emits.
		Mark Kac has shown that the area, circumference, and the number of holes in the membrane can be recovered from the expansion in powers of t of the trace of the heat equation in the membrane.
	www.iit.edu /~am/events/schuss2_abs.html (224 words)

	CAN YOU HEAR THE SHAPE OF A DRUM?
		A (simply connected) planar drum is obtained by taking a loop of wire, bending it into any shape that can be laid flat on the table, and stretching a drum skin across it.
		Some people have better hearing than others, and whereas a person with good hearing might be able to tell two drums appart, they might sound identical to someone whose hearing is not so good.
		Mathematicians try to answer the question in an idealized situation, where an idealized note is determined from the shape of the drum by a mathematical process.
	math.ucsd.edu /~okikiolu/projects/drum.html (712 words)

	[No title]
		You Cannot Hear the Shape of a Two-Piece Band A two-piece band is a union of two drums.
		Drums in the Photograph of Carolyn Gordon and David Webb Since Carolyn Gordon was looking for soundalike drums, she had to find two drums with the same area and perimeter that also sounded the same when they were played.
		Have them fold this drum in order to make five pieces so that two are crosses of the same size, and the other three are halves of a cross (split along the diagonal of the square in the middle of a cross).
	www.mathsci.appstate.edu /~sjg/ncctm/ncctmdrums.doc (2722 words)

	On Hearing the Shape of a Drum, Applied to Finding the Shape of aQuantum Box by it's Energy Eigenstates
		We are given a two dimensional drum with a membrane stretched over it's surface.
		If we are given a drum shape, we can apply the laws of physics to determine what that drum will sound like; this is the application of the familiar wave equation.
		There is one case, however, in which we can tell the exact shape of the drum, and the problem remains solvable.
	bea.st /text/drum/drum.html (1358 words)

	Hearing the Shape of Drums (Site not responding. Last check: 2007-11-05)
		While the theorem of isospectral domains was proved on abstract mathematical grounds, the actual resonance frequencies and wave functions of the geometries were not known.
		The resonances were obtained by actually constructing the shapes using copper.
		Therefore these experiments were not only able to physically realize drums which sounded alike, but also were able to show that there were no degeneracies in the first 54 resonances.
	sagar.physics.neu.edu /isospec.html (213 words)

	Howstuffworks "How Hearing Works"
		This could be a solid, such as earth; a liquid, such as water; or a gas, such as air.
		In reality, these tubes are coiled in the shape of a snail shell, but it's easier to understand what's going on if you imagine them stretched out.
		It's astonishing how much is involved in the hearing process, and it's even more amazing that all these processes take place in such a small area of the body.
	www.howstuffworks.com /hearing.htm/printable (2508 words)

	Hearing the shape of a drum - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab-3.cs.princeton.edu) (Site not responding. Last check: 2007-11-05)
		To hear the shape of a drum is to infer information about the shape of the drumhead from the sound it makes, i.e., from the list of basic harmonics, via the use of mathematical theory.
		Michel L. Lapidus, Vibrations of fractal drums, the Riemann hypothesis, waves in fractal media, and the Weyl-Berry conjecture, in: Ordinary and Partial Differential Equations (B. Sleeman and R. Jarvis, eds.), vol.
		Michel L. Lapidus and Carl Pomerance, The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums.
	en.wikipedia.org.cob-web.org:8888 /wiki/Hearing_the_shape_of_a_drum (832 words)

	Incorporating the Mathematical Achievements of Women and Minorities into Schools: Columns and Classroom Activity Sheets
		NCCTM Centroid Column on Hearing the Shape of a Drum
		Includes a description of research showing that incorporating the mathematical achievements of women and minorities into school classrooms is beneficial to ALL students, and ways to include ideas related to the research of Carolyn Gordon and Kate Okikiolu into classrooms.
		Drums in the photograph of Carolyn Gordon and David Webb
	www.mathsci.appstate.edu /~sjg/ncctm/activities (472 words)

	Vibrating Drum
		On hearing the shape of the three-dimensional multi-connected vibrating membrane with piecewise smooth boundary conditions.
		Estimate on the fundamental frequency of a drum.
		On hearing the shape of a drum: An extension to higher dimensions.
	math.fullerton.edu /mathews/n2003/vibratingdrum/VibratingDrumBib/Links/VibratingDrumBib_lnk_2.html (456 words)

	Drum Links
		By the time I was born in 1965, drums was firmly in place as the family business.
		My dad sold all of the major brands of the time, and it was a great place for all of the local drummers and his students to hang out and talk drums.
		As you can see, I have a passion for drums that runs very deep, it is a business that my family has been involved in for many years, and providing this service on the internet couples it with technology, which is also a big part of my life.
	www.drumchops.com /bio.html (1014 words)

	SPAMS Email Archive - Alexey Spiridonov - Can you hear the shape of a (discrete) drum? (Site not responding. Last check: 2007-11-05)
		He's going tell us about a classic applied math problem; so bring your hearing aides and see if you can hear the shape of a drum.
		His conjecture was not without cause: it was known at the time that the sound spectrum of a drum beat encodes the drum's area, perimeter and genus.
		Well, differential geometers make drums from leather, whereas we'll make do with fabric (conveniently approximated by a graph on a lattice).
	www-math.mit.edu /spams/spring2005/email12.htm (260 words)

	Hearing Shapes in ZhurnalWiki (Site not responding. Last check: 2007-11-05)
		The topic was "Can You Hear the Shape of a Drum?" In other words, what information is carried by the overtones of a vibrating membrane?
		Amazingly enough, one can "hear" a lot: the total surface area, the circumference, and the number of holes in the drumhead, for starters.
		(To a mathematician the drum needn't be circular, or even a solid sheet of material.) The various normal modes of oscillation for a thin film under tension somehow encode a host of detail about the object.
	zhurnal.net /ww/zw?HearingShapes (248 words)

	MetalReview.com - Metal Review of Dynamic Lights - Shape (Site not responding. Last check: 2007-11-05)
		Vocalist Matteo Infante is a near dead ringer for James LaBrie, but occasionally we hear him channel the overdramatic aura of Tom S. Englund or the steel pipe bark of Russell Allen.
		Setting the tempo for the rest of the band, he has a style of drumming that is reminiscent of Mike Portnoy and yes, even Neal Peart.
		As cliché as it may be, all but two of the eight compositions on Shape clock in between six and twelve minutes in length, with “One Thousand Nothing” and “In The Hands Of A Siren” being the most mammoth tracks on this disc.
	www.metalreview.com /viewreview.aspx?ID=1694 (669 words)

	Harmonic Analysis -- from Wolfram MathWorld
		As a result, the mathematical study of overlapping waves is called harmonic analysis.
		Harmonic analysis is a diverse field including such branches as Fourier series, isospectral manifolds (hearing the shape of a drum), and
		Signal processing, medical imaging, and quantum mechanics are three of the fields that use harmonic analysis extensively.
	mathworld.wolfram.com /HarmonicAnalysis.html (109 words)

	[No title]
		Show f_n are an equicontinuous family, that there exists a function f which is analytic to which the f_n converge.
		A: Aizenman began to ask some strange question about hearing the shape of a circular drum.
		I started walking towards him expecting to hear "You Failed!" Instead he said "Congratulations." I said "What?" He said "You passed." My response was: "How!?" He said "Your not the only one who forgets how to think when they're under pressure." All in all, it was a grueling experience.
	www.princeton.edu /~missouri/Generals/generals/asok_aravind (1277 words)

	ooBdoo
		Several American Indian-style drums for sale at the National Museum of the American Indian.
		This audio file was created from an article revision dated 2005-04-13, and does not reflect subsequent edits to the article.
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	www.oobdoo.com /wikipedia/?title=Drum (711 words)

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