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AP Physics 2: 1.2 Waves
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AP Physics 2: 1.2 Waves. What is the mathematical description of the wave?

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AP Physics 2: 1.2 Waves 172 Views


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Description:

AP Physics 2: 1.2 Waves. What is the mathematical description of the wave?

Language:
English Language

Transcript

00:00

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

00:06

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

00:09

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

00:12

the standing wave Why of x t equals four sign

00:17

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

00:21

propagating but otherwise identical waves Well one of these why

00:27

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

00:31

the mathematical description of the other wave Why x t

00:35

and here are potential answers All right here we go

00:42

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

00:45

it We get to talk about trig identities We know

00:49

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

00:52

loud Scary house to figure this out were specifically talking

00:57

about some and difference formulas But we know a standing

01:00

wave is really two waves moving in opposite directions creating

01:04

nodes of maximum destructive interference An anti nodes of maximum

01:09

construct of interference Well a standing wave of why ext

01:12

is described as a sign b plus c plus a

01:17

sine b minus e And to expand that further equals

01:21

a sign of pecos Nc plus coastline be signed c

01:26

plus eight times quantity and quality signed b cosign c

01:30

minus co signed b sci fi and your skin is

01:33

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

01:35

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

01:38

equations with the distributive property and then we can see

01:42

that the two versions of a co sign be sine

01:45

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

01:48

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

01:52

co signed c well we were given y of x

01:56

Equals four sign three t co signed seven x at

01:59

the start of the equation we can set that equation

02:02

is equal to what we just put together with that

02:05

we can find that a equals to be equals three

02:08

t and c equal seven x this means that why

02:12

x t equals to sign three t plus seven x

02:15

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

02:19

at the equation we found and looking at the answer

02:21

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

02:24

way of travelling in the negative direction has to either

02:27

be to sign three tea plus seven Acts or to

02:30

sign 3 team minus seven x the only thing we

02:33

have to figure out now is the direction well because

02:36

this wave moves in the negative x direction as time

02:39

increases the accent e coefficients need tohave the same sign

02:43

and that means the answer is b remember the wave

02:48

moving in the positive ex direction will always have the

02:51

format of why x minus t on the wave moving

02:55

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

02:58

why x plus team okay that was a lot of

03:01

trick identity work were emotionally drained from all the fun

03:04

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

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