ShmoopTube

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Fine we sneak And here's your shmoop to shore brought

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to you by standing waves But we're feeling lazy right

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now so we'll just wave from our chair I consider

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the standing wave Why of x t equals four sign

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three t co signed seven x it's formed by counter

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propagating but otherwise identical waves Well one of these why

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of ext is travelling in the positive ex direction what's

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the mathematical description of the other wave Why x t

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and here are potential answers All right here we go

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Homeboy we're so excited for this We can barely stand

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it We get to talk about trig identities We know

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we're stuff too but trying to scream with joy too

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loud Scary house to figure this out were specifically talking

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about some and difference formulas But we know a standing

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wave is really two waves moving in opposite directions creating

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nodes of maximum destructive interference An anti nodes of maximum

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construct of interference Well a standing wave of why ext

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is described as a sign b plus c plus a

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sine b minus e And to expand that further equals

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a sign of pecos Nc plus coastline be signed c

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plus eight times quantity and quality signed b cosign c

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minus co signed b sci fi and your skin is

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we're right down there right All right that's a mouthful

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and that'll wear out of tongue We can simplify the

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equations with the distributive property and then we can see

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that the two versions of a co sign be sine

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c cancel each other out since we're subtracting one of

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them So we're left with two of a sign be

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co signed c well we were given y of x

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Equals four sign three t co signed seven x at

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the start of the equation we can set that equation

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is equal to what we just put together with that

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we can find that a equals to be equals three

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t and c equal seven x this means that why

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x t equals to sign three t plus seven x

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plus to sign three team minus seven x We're looking

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at the equation we found and looking at the answer

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we've already rule out a nd we know that the

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way of travelling in the negative direction has to either

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be to sign three tea plus seven Acts or to

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sign 3 team minus seven x the only thing we

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have to figure out now is the direction well because

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this wave moves in the negative x direction as time

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increases the accent e coefficients need tohave the same sign

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and that means the answer is b remember the wave

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moving in the positive ex direction will always have the

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format of why x minus t on the wave moving

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from right to left We'll always have the format of

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why x plus team okay that was a lot of

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trick identity work were emotionally drained from all the fun

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we just had All we can muster is a lying 00:03:07.395 --> [endTime] down wave Now Yeah

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