Question

Someone please help! :/

Answer 1

@acxbox22 @zepdrix @Nnesha

Answer 2

@freckles

Answer 3

^ freckles, sorry, I know you juust got on. But I need help! :/

Answer 4

hrm, ok.

Answer 5

I'm reading a little about this.
I think I understand this so far:
the nodes happen when sin(ax)=0
that is when ax=npi where n is an integer
or x=npi/a ( I just divided both sides by a here)
we have our nodes occur at x=0,pi/2,pi,3pi/2,2pi
see if you can use this to find your a

Answer 6

or alpha is what they call it

Answer 7

hm how?

Answer 8

well you have x=npi/a
for n=0 that is x=0
for n=1 that is x=pi/a and you had your next node is x=pi/2
for n=2 that is x=2pi/a and you had your next next node is x=pi (or you can write pi as 2pi/2)
for n=3 that is x=3pi/a and you had your next next next node is x=3pi/2
and so on...

Answer 9

can you see what a is yet?

Answer 10

a is alpha?

Answer 11

yes a is alpha
but what is alpha?

Answer 12

x=pi/a means that ax=pi...

Answer 13

bleh, sorry i'm being so slow =.=

Answer 14

have you compared any of the values I asked you too?

Answer 15

like pi/a to pi/2
and 2pi/a to pi
and 3pi/a to 3pi/2
and 4pi/a to 2pi

all of these comparisons should tell you a is ....

Answer 16

I ..really have no idea. I'm blank.

Answer 17

so you cannot think of any value a such that
pi/a would be the same as pi/2 ?

Answer 18

2?

Answer 19

yes if a is 2
all of those would hold as equations
all of those would hold as our nodes
like if a=2 then you have the following nodes
(n=0) ->0*pi/2=0
(n=1) ->1*pi/2=pi/2
(n=2) ->2*pi/2=pi
(n=3) ->3pi/2
(n=4) ->4pi/2=2pi

Answer 20

and we were already given the big value A

Answer 21

now we have to find beta which I will call b

Answer 22

ok.

Answer 23

so what does your equation look like so far?

Answer 24

y(x,t)=A sin k(x-vt)+ A sin k(x+vt)
=2A sin kx cos kvt
is the equation?

Answer 25

oops, sorry wrong one.

Answer 26

y= 7sin (2x) cos(bt)

Answer 27

right? alpha is 2?

Answer 28

great not we have to somehow find b
and yes remember we found alpha (a) by solving the node equation
sin(ax)=0
which is when ax=npi (n is integer)
so dividing a on both sides givens x=npi/a
then we just compared this to the nodes given to find a

Answer 29

any ideas on how to find b

Answer 30

uh. B is the horizontal stretch yeah?

Answer 31

1=cos(bt) at pi/4

Answer 32

that is true
let me think hmm..
cos(bt)=1 when
bt=2npi where n is an integer
so
t=2npi/b

let me think or you can think
can we use this?

Answer 33

well..the cosine will keep equaling to zero then.

Answer 34

cos^-1(x) = 0

Answer 35

why is that ?

Answer 36

that's just what it equals..I think ??

Answer 37

hey

Answer 38

I think it is simpler than we are making it

let's look at the example

Answer 39

notice one cycle has length 10
but the overall length is 30
so 30/10 is 3 and that is there beta (or b)

Answer 40

notice one cycle in our graph has length pi
and 4pi is suppose to be the overrall length

Answer 41

so 4pi/pi is what I think our b is

Answer 42

ooh 4pi going and coming back ??

Answer 43

frequency = reciprocal of period

Answer 44

I am soo sorry this has taken so long. It's due tomorrow and i'm just super frustrated with it. You've been amazing.

Answer 45

sorry my internet broke or something

Answer 46

well i'm still kinda confused about beta
I think it is 4

maybe @dan815 can confirm or not

Answer 47

It's all good. haha ok. I think tomorrow morning i'll try to go to the math tutoring place too but idk if i'll have time before it's due D:

Answer 48

@wio do you know about these standing wave type graphs?

Answer 49

lol I'm going to take that back and put here what I deleted earlier
at x=pi/4 y isn't always 7
t moves the y up and down
so we did have at x=pi/4
\[y(t)=7 \cos(bt) \\ \text{ and period of consine function is suppose to be } \frac{2 \pi}{b} \\ \text{ put we have this should be } 4\pi \\ \frac{2\pi}{b}=4 \pi \\ 2\pi =4 \pi b \\ \frac{2 \pi}{4 \pi}=b \\ \frac{1}{2}=b\]
like I was wrong earlier I think
t only effects the up and down part

but I also still might have a wrong interpretation

and here is where I give up
and hope you will come back and tell me how to find b

Answer 50

^^ thanks so much. That's a huge help even if it's not completely solved :)

Answer 51

@freckles is correct and b=1/2 is the right ans...

note the expression given y(x,t)=Asinaxcosbt, the cosbt description a cyclical variation with b as its angular frequency. b is related to the period, T, by the eqn
b=2pi/T.

as T=4pi, b=1/2 :)

Answer 52

@freckles ahh you were right, when I looked at it this morning it all made sense. I Was just too frustrated and exhausted I think. thanks so much for coping with me and helping out!
@sdfgsdfgs thank you too!

Answer 53

the final equation is: y(x,t) = 7 sin 2x cos (t/2)

Answer 54

yeppers!
and thanks for confirming my thoughts on the problem @sdfgsdfgs
I was kinda unsure :p

Answer 55

and np it was fun to learn something sorta kind of new @babynini

Answer 56

^ haha that's the attitude! xP Well, now it'll be ingrained into our minds forever (or at least until after the next exam ;))

Answer 57

lol