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Ernst Mach

Mach wanted to check thc rcliability of Melsenss conclusions. Mach’s own background in ballistic cxpcrimcntation was cxtensivc, cspccially conccrning thc spccd of projcctilcs and trying to photograph ihcm i_n motion.⁴ Hc had also learncd a grcat dcal from other cxpcriments on rapid motion, such as thosc conccrncd with thc Doppler theory (x86o 1878), blood pressure mcasuring Instruments (1862), liquid pressure in pipcs (1862), acoustic wavcs in thc human car (1863), thc efTccts of sound wavcs on glass and quartz (1872), and soot, clcctric spark, and explosion cxperimcnts (1875)/’ Equally valuable was thc cipericnce hc had gaincd from construaing (logether with his laboratory hclpcr Franz Hajck) laboratory cquipmcnt that could measurc rapid motion.

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We norinally think of electric sparks as flashes of light, but with care they can often bc hcard as well. In a sensc they are miniaturę explo-sions that give olT audible waves which Mach naturally supposcd could not cxcecd tlić spccd of sound. In 1875, Machs assistant Ćcnek I)vorak brought to his attention an article by K. Antolik. The articlc “Acoustic Phcnorncna of Electric Spark Discharges" stimulatcd Mach to make a scries of curious expcriments. Since we know thc spccd of sound, thc measured distancc that thesc spark waves travcl should givc us an exact mcasurement of time. Mach went to work to build a suitablc “time machinę," or rather, time measuring apparatus. But something went decidcdly wrong.

Mach had dcviscd a tcchnique whereby spark wavcs would blow soot across a glass platc. If thcrc wcrc two sparks separated at a distance from cach other then thc wavcs would canccl cach other out and a soot linę would bc formed. If thc sparks were dischargcd at thc same time then thc linc should prcsumably be halfway between them.

In one cxperiment he uscd a flying bullct to discharge both sparks, with a ballistic pcndulum to mcasurc the exact spccd of thc projcctilc. This gave an exact delay time, but unfortunatcly, thc soot linc did not form thc cxpcctcd pattern. Two unanticipated “V" angles appeared fscc diagram 4). On close examination it was discovcrcd that thc spark wavc had gont faster than thc speed of sound! Hencc, it could not be an acoustical wave in any normal sensc, evcn if it was audible. It was, in fact, a shock wavc. The discovcry ruined Mach’s “time machinę,“ but it cxcited his imagination to procced further.

Mach ShocĄ Waues

Anothcr pcculiarily soon turned up. Spark (i.c„ shock) waves bounccd otf a pcrpcndicular wali in cxpcctcd fashion, that is, as normal sound waves do. hut whcn thc wali was tiltcd bcyond a ccrtain anglc a strangc cfTcct took place. A three-front or Y soot pattern rcsultcd with a primary front, a rcflcctcd front, and a doubly rcflcctcd front (scc diagram 5). Mach published these rcsults in an 1878 articlc.** Dr. Merz-kirch bas dcscribcd Mach’s ncw discovcry as follows:

flcctcd." ⁷

According to Mach thc intcrscction of thc two wavcs of finitc amplitudę bccomcs thc origin of a ncw wavc which travcls along thc primary wave front with a ccrtain vdocity w. Whcn thc velocity componcnt of thc sccon-dary wavc parallcl to thc dircction of motion of thc primary wavc, » cos (f/2)» cxcccds thc spccd W if thc primary wavc, then thc Y-shaped sepa-ration is supposcd to start, and thc irrcgular rcflcction begins. It is possiblc to dctcrminc for givcn W and w a limiting anglc (₀ beiow which thc rcgular rcflcction cannot cxist. W, _w and hcncc also (_Q arc functions of thc shock strength. The phenomenon is thc same whcn thc axis is rcplaccd by a solid wali, at which thc blast wavc originating from one spark gap is now re-

Machs namc gradually bccamc associatcd with a number of soot wavc and anglcd wali phenomena.⁸

Mach’s soot cxpcrimcnts werc important both in thcmsclvcs and in preparing him for his latcr major shock wavc discovcries.^tt With rcspect to Mach labcls, Raymond J. Scegcr during World War 11 scems to havc becn thc first to give published rcfcrence to thc cxpressions "Mach efTect" and "Mach rcflcction.” ^l" The term “Mach stem" has gaincd a measurc

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Double "V" Diagram.

The two soot linc anglcs (Mach effeets) arc joined by a soot linc (Mach bridge) halfway between A and B The letters represent simultancous cxplosion points.

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