Undergrad Clarification for a standing wave on a string equation

[rudy]

Hello,

Came across https://drive.google.com/file/d/1bpB7BcVf1yQLiwg9quAn2vlhu8-i6Zy_/view and I'm not sure about one thing

For the 2 parts of the equation with sin, is it:
1. [...sin(kx)]sin(wt)

or is it:
2. [...sin(k)*x]sin(w)*t

Thank you

-DR

 

[jtbell]

First, a friendly tip about images: use the UPLOAD button at the bottom of the posting box, then use the option to display as a full image instead of a thumbnail. Then people can see the image directly and don't have to click the link to access your Google Drive.

The answer to your question is choice "1."

 

[jishnu]

Hello,

Came across https://drive.google.com/file/d/1bpB7BcVf1yQLiwg9quAn2vlhu8-i6Zy_/view and I'm not sure about one thing

For the 2 parts of the equation with sin, is it:
1. [...sin(kx)]sin(wt)

or is it:
2. [...sin(k)*x]sin(w)*t

Thank you

-DR

I am unable to understand what actually is you doubt regarding the standing waves, please make it clear in the post.

 

[rudy]

Sorry about that... I did try to upload but when I previewed my post I kept getting a "broken image link" symbol (does the image only appear once the post is published?)

And to clarify my question, I was wondering if the variables (x and t) are included inside the sine function parenthesis or if it is multiplied separately.

I'll rewrite 2. as:
[...x*sin(k)]t*sin(w)

and 1. was:
[...sin(kx)]sin(wt)

thanks jt

 

[jishnu]

Sorry about that... I did try to upload but when I previewed my post I kept getting a "broken image link" symbol (does the image only appear once the post is published?)

And to clarify my question, I was wondering if the variables (x and t) are included inside the sine function parenthesis or if it is multiplied separately.

I'll rewrite 2. as:
[...x*sin(k)]t*sin(w)

and 1. was:
[...sin(kx)]sin(wt)

thanks jt

1 is right, the variables x and t should be within the sine function parenthesis.

 

[sophiecentaur]

If you look at 1., it describes a function that has k cycles per metre and a time variation that's proportional to ω. This describes a function with a range of frequencies and nodes.; it looks like a wave of some sort. The other expression (2.) has the k and ω inside the sin functions. These are both constants and so are sin(k) and sin(ω) so it doesn't describe a function that varies at all! It can't be a wave.
It's important to try to interpret what a formula actually does when you can. It gives a good insight into the relationship between the Maths and the Physics of a situation. It can be worth while even when some of the functions are not familiar.