Mechanické vlnění
2. Mechanické vlnění
2.1 Vznik a druhy vlnění
2.2 Rovnice postupného vlnění
2.3 Interference vlnění
2.4 Lom a odraz vlnění
2.5 Ohyb vlnění
2. Mechanické vlnění
- Jeden z nejčastějších fyzikálních jevů
- Zvuk, radiové vlny, mikrovlny, světlo, televizní vysílání
- Vlnění mají různou fyzikální podstatu, ale platí pro ně řada společných zákonitostí
- Kmitání šířící se prostorem od zdroje všemi směry
- Dochází k přesunu energie, ne hmoty
- Podstatou mechanického vlnění je přenos kmitání látkovým prostředím, šíření vln není spojeno s přenosem látky, vlněním se však přenáší energie
2.1 Vznik a druhy vlnění
- Vzniká v látkách všech skupenství
- Příčinou existence vazeb mezi částicemi prostředí
Vlnová délka
- Fyzikální veličina
- l [m]
- Vzdálenost, do které se rozšíří vlnění za dobu jedné periody
- l = vT = v/f
Druhy vlnění
1) Postupné
a) Příčné – částice kmitají kolmo na směr vlnění (hadice, lano)
b) Podélné – částice kmitají ve směru, kterým vlněný postupuje (pružina)
2) Stojaté – viz. Interference
Rychlost vlnění
- Závisí na vlastnostech pružného prostředí (skupenství)
2.2 Rovnice postupného vlnění
- Vztah umožňující okamžitou výchylku v každém bodě řady, kterou se vlnění šíří
- Tato výchylka závisí na čase t a na vzdálenosti x od zdroje vlnění
- Y = ymsinwt – pro kmitání
- t= x/v
Rovnice postupné vlny
- Y = ymsin2p(t/T – x/t)
- Platí pro příčné i podélné vlnění
- 2p(t/T – x/t) – fáze vlnění (¡)
2.3 Interference vlnění
- Interference = skládání vlnění
- V místech, kde se vlny překrývají pozorujeme, že má amplituda různou velikost
- Jednotlivé výchylky se sčítají
- Princip superpozice
- O výsledku vlnění y1 a y2 rozhodne jejich fázový rozdíl ¡
- D¡ = 2p/x.d – d= x1 – x2 = dráhový rozdíl – vzdálenost dvou bodů, které kmitají se stejnou fází
Zvláštní případy interference
- Nastávají, když je dráhový rozdíl roven celistvému počtu půlvln interferujících vlnění
1) Sudý počet půlvln
- D = 2kl/2 = kl
- Interferující vlnění se setkávají v každém bodě se stejnou fází ® vzniká interferenční maximum
2) Lichý počet půlvln
- D = (2k+1)l/2
- Interferující vlnění se setkávají s opačnou fází ® interferenční minimum
- Interferencí dvou vlnění o stejné vlnové délce, vzniká výsledné vlnění, jehož amplituda je největší v bodech, kde se setkávají se stejnou fází a nejmenší tam, kde se setkávají s fází opačnou
- Interference rozhodne zda má zkoumaný jev vlnovou povahu (interference světla)
Stojaté vlnění
- Vzniká interferencí 2 vlnění
- Průběh vlnění vytváří dojem jako by vlna na vlákně stála a nepohybovala se
- Zdroj – uzel = l/2
- Zdroj – kmitna = l/4
- Uzel = místo, kde je výchylka minimální – těleso nekmitá
- Kmitna = místo, kde je výchylka maximální
Rozdíl mezi postupným a stojatým vlněním
- Při postupném vlněním všechny body kmitají se stejnou amplitudou, ale různou fází, přenáší se energie
- Při stojatém vlnění se energie nepřenáší, jen se periodicky mění potenciální energie pružnosti v kinetickou energii, všechny body kmitají mezi dvěma uzly se stejnou fází, ale s různou amplitudou
2.4 Odraz a lom vlnění
- izotropní prostředí = z hlediska šíření vlnění má ve všech bodech i směrech stejné vlastnosti
- vlnoplocha = plocha, jejíž body kmitají se stejnou fází
- vlnění se šíří ve směru paprsku, který je vždy kolmý na vlnoplochu
Huygensův princip
- každý bod vlnoplochy do něhož dospělo vlnění v určitém okamžiku můžeme pokládat za zdroj elementárního vlnění, které se z něho šíří v elementárních vlnoplochách. Vlnoplocha v dalším časovém okamžiku je vnější obalová plocha všech elementárních vlnoploch
- určuje jak určit tvar vlnoplochy v určitém předcházejícím okamžiku
Odraz vlnění
- řídí se zákonem odrazu: úhel odrazu je roven úhlu dopadu
- odražený paprsek zůstává v rovině dopadu
- k odrazu dochází, jestliže se vlnění dostane k pevné překážce
Lom vlnění
- projevuje se změnou směru, kterým se vlnění po průchodu rozhraním dvou prostředí šíří
- lom mechanického vlnění většinou nepozorujeme, mnohem větší význam má lom světla
2.5 Ohyb vlnění
- vlnění se může šířit i za překážkou
- poměrně složitý jev, pomocí Huygensova principu lze objasnit jen jeho podstatu
- každý bod vlnoplochy, která dospěla k překážce je zdrojem elementárního vlnění, které se šíří všemi směry, tedy i do prostoru za překážkou
- ohyb je tím výraznější, čím větší je vlnová délka vlnění
- výrazně se ohyb projevuje u zvuku než u světla
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