Max amplitude of superposition of 2 waves

[rc2008]

Homework Statement

Max amplitude of superposition of 2 waves

Relevant Equations

Find amplitude of superposition of 2 waves, 4.6sin 2pi()*5.4x and 3.2sin2pi()*10x,

My answer is simply 4.6+ 3.2 = 7.8m , correct me if I am wrong.

If it's 4.6 $\cos(2\pi*5.4x)$ and 3.2 $\sin(2\pi*10x)$, then the max amplitude should be sqrt(4.6^2 + 3.2^2) = 5.6m, correct me if I am wrong.

 

[BvU]

Hi, and ,

I can't even read your formulas (surely you don't mean $(\sin 2)\ \pi \ 10x$ but what you do mean is a guess.

Use some more brackets and learn to use $\TeX$

And your two claims cannot both be correct !

If it's 4.6cos2pi()*5.4x and 3.2sin2pi()*10x, then the max amplitude should be sqrt(4.6^2 + 3.2^2) = 5.6

What mathematical rule are you using here ?

And a graph of the superposition easily proves it's wrong !

$\$

 

[BvU]

What do you get for the amplitude of $\cos x+\sin x\$ ? For $\cos x+\sin (2x)\$ ?

$\$

 

[rc2008]

What do you get for the amplitude of $\cos x+\sin x\$ ? For $\cos x+\sin (2x)\$ ?

$\$

For $\cos x+\sin x\$, i would get 2 , simply because $sqrt(1+1)$ = 2

 

[rc2008]

What do you get for the amplitude of $\cos x+\sin x\$ ? For $\cos x+\sin (2x)\$ ?

$\$

For $\cos x+\sin (2x)\$, I would also get 2, simply because of shape of $\cos (x) \$ will coincide after some time.

For my case of
4.6 $\cos(2\pi*5.4x)$ and 3.2 $\sin(2\pi*10x)$
, I am not sure whether they will coincide or not because 10 is not a whole numer of multiplier of 5.4

 

[BvU]

For $\cos x+\sin x\$ , i would get 2 , simply because sqrt(1+1) = 2

sqrt (1+1) = 2 ?
Ah, you are learning $\TeX$ ! Bravo !

For $\cos x+\sin (2x)\$, I would also get 2, simply because of shape of $\cos (x) \$ will coincide after some time.

For my case of
4.6 $\cos(2\pi*5.4x)$ and 3.2 $\sin(2\pi*10x)$
, I am not sure whether they will coincide or not because 10 is not a whole numer of multiplier of 5.4

You must have seen plots of $\sin x$ and $\cos x$.

$\cos x+\sin (2x)\$ looks like this:

Functions coincide some times (with y=0), peaks don't !

 

[Mark44]

For $\cos x+\sin x\$, i would get 2 , simply because $sqrt(1+1)$ = 2

That's not true at all.
$\sqrt{1 + 1} = \sqrt 2$.

Here's my LaTeX before it gets rendered by the browser: $\sqrt{1 + 1} = \sqrt 2$

Notice the backslash in front of the sqrt command.

 

[BvU]

My answer is simply 4.6+ 3.2 = 7.8m , correct me if I am wrong.

What condition(s) has(have) to be fulfilled for this 7.8 to be the value of $4.6 \cos(2\pi*5.4x) + 3.2\sin(2\pi*10x)$ ?
And for -7.8 ?

$\$

 

[pasmith]

4.6 \cos(2\pi*5.4x) + 3.2\sin(2\pi*10x) is periodic, because 5.4 is a rational multiple of 10. (It would be easier to write this as 4.6\cos(10.8\pi x) + 3.2\sin(20\pi x).)

It is not in general possible to reduce sines of different frequencies to an expression of the form R\sin (\alpha x + \beta). It might be possible to obtain the zeros of the derivative analytically, but most likely a numerical method will be required.

 

[WWGD]

That's not true at all.
$\sqrt{1 + 1} = \sqrt 2$.

Here's my LaTeX before it gets rendered by the browser: $\sqrt{1 + 1} = \sqrt 2$

Notice the backslash in front of the sqrt command.

How do you prevent the Latex from rendering, even when using tags?

 

[Mark44]

How do you prevent the Latex from rendering, even when using tags?

For the stuff I don't want to render, I color the first # of each group black using the BBCode color tool.