Question

A Standing wave. Trig help!

Answer 1

I am trying to find an example in my book, one moment.

Answer 2

Ok :)

Answer 3

hmm, my book says:
"If there are two waves traveling along the same string, then the movement of the string is determined by the sum of the two waves. For example, if the string is attached to a wall, then the waves bounce back with the same amplitude and speed but in the opposite direction. In this case, one wave is described by
y=A sin K (x-vt) and the reflected wave by
y= A sin K(x+vt). The resulting wave is

y(x,t)=A sin k(x-vt)+ A sin k(x+vt) [add the two waves]
=2A sin kx cos kvt

Answer 4

[sum-to-product formula] is the second =

Answer 5

lets look at one wave
y(x,t)= 7 sin (1/2 ( x - vt ) )

Answer 6

A would be 7 because that is the amplitude of the wave

Answer 7

not sure how to eliminate v

Answer 8

I'd the period is 4π then the frequency is 1/4π.
β=ω = 2πf = 1/2

Answer 9

Wait the problem says the period is 4pi but the picture shows it as pi

Answer 10

Sinαx = 0 when x=0,π/2 &π
so α=2

Answer 11

The graph is for y&x

Answer 12

and alpha = k?

Answer 13

the given period is 4pi so I would do
2pi/k = (2pi)/(4pi) and the period ends up being 1/2?

Answer 14

I'm still confused as to why they say the period is 4pi if it's pi in the pic o_0

Answer 15

im going to come back to this, be right back

Answer 16

k

Answer 17

@zepdrix I promise I dont' know how to do this one. xD

Answer 18

If you're at all familiar with the graph of the sine wave, you can immediately remove the cosine factor by setting \(\beta=0\). As someone mentioned above, \(A=7\) guarantees an amplitude of \(7\).

As for the period, you're right, it's \(\pi\), which means \(\alpha\) should satisfy \(\dfrac{2\pi}{\alpha}=\pi\).

Answer 19

Then again, that's the period if you just refer to the graph and not the given information.

Answer 20

That info could amount to a typo. If the nodes are as listed (and they agree with the graph), then the period is indeed \(\pi\), not \(4\pi\).

Answer 21

hm, ok :)

Answer 22

so, so far I have
y= 7sin(ax)cos(beta(t))
how do I fill in all that?

Answer 23

@SithsAndGiggles

Answer 24

@FibonacciChick666

Answer 25

Sorry, trig was 10th grade(8ish years ago).... I don't remember that.

Answer 26

aw man haha, well thanks anyway.

Answer 27

I've already given you the values for α and β!

Answer 28

^^ thanks alekos. I didn't see that before, oopsies.