Cov txheej txheem:
Video: Cardioid zoo li cas?
2024 Tus sau: Michael Samuels | [email protected]. Kawg hloov kho: 2023-12-16 01:44
A daim cardioid (los ntawm Greek καρδία "lub plawv") yog lub dav hlau nkhaus taug los ntawm ib qho taw qhia ntawm ib puag ncig ntawm lub voj voog uas tau dov ib ncig ntawm lub voj voog ruaj khov ntawm tib lub vojvoog. Hauv peb qhov loj me, cov daim cardioid yog zoo li ib lub kua nyob nruab nrab ntawm lub microphone uas yog "stalk" ntawm cov kua.
Thiaj li, koj yuav xam cardioid li cas?
Yog tias lub vojvoog ntawm lub voj voog uas tsim cov cardioid yog a, tom qab ntawd peb muaj cov hauv qab no:
- Qhov sib npaug ntawm kab rov tav cardioid yog r = a ± acosθ.
- Qhov sib npaug ntawm cardioid ntsug yog r = a ± asinθ.
Tsis tas li, qhov sib txawv ntawm cardioid thiab Limacon yog dab tsi? Thaum tus nqi ntawm a tsawg dua tus nqi b, daim duab yog a limacon nrog thiab sab hauv lub voj. Thaum tus nqi ntawm a ntau dua li tus nqi b, daim duab yog dimpled limacon . Thaum tus nqi ntawm qhov sib npaug tus nqi ntawm b, kab lus yog qhov xwm txheej tshwj xeeb ntawm limacon . Nws hu ua a daim cardioid.
Kuj paub, thaj tsam ntawm cardioid yog dab tsi?
Nrhiav qhov thaj tsam sab hauv daim cardioid r = 1 + cos θ cov. Teb: Cov daim cardioid yog li muaj npe vim nws zoo li lub plawv. Siv kab txaij radial, qhov txwv ntawm kev koom ua ke yog (sab hauv) r ntawm 0 txog 1 + cos θ; (sab nrauv) θ ntawm 0 txog 2π. Yog li, cov thaj tsam yog ?? ? 2π? 1+cos θ dA = r dr dθ.
Leej twg pom qhov nkhaus cardioid?
Nws qhov ntev tau pom los ntawm Phillipe de la Hire hauv 1708. Cardioid yog qhov xwm txheej tshwj xeeb ntawm limacon ntawm Pascal: tsev neeg ntawm nkhaus kawm thiab npe tom qab Étienne Pascal (1588 txog 1640), leej txiv ntawm Blaise Pascal (1623 txog 1662).
Pom zoo:
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