Physics and standing waves on a string

[Slapper]

Taking Physics and one of the questions asks what a standing wave pattern would look like if the string was made from one thick string and one thin string. I say the wave pattern would just be the average of the two strings, but I'm no Physicist.

[Thuronn]

lol.

This will help solve some of the problems in String Theory. Thank you for contributing to the ever growing field of Theoretical Physics.

[Slapper]

String theory? I'm talking about hooking an actual piece of string made up of two different strings, hook it up to a mechanical oscillator, which is hooked up to a signal generator to control the frequency of the waves traveling through the string, then have a hanging mass at the end of the string. I'm asking what the wave pattern would look like on the string (if the wave is just the average of the two strings or there's two different waves).

http://img72.imageshack.us/img72/7813/string.png

[Jefe]

Eh, no need to be a physicist or w/e. Anyway, where is the pulse coming from, the light string or thick string, because you'll get different results.

String theory is some other shit, an 11th dimension is introduced, etc.

Edit: Eh, ok. If the incident pulse is traveling along the thin string once it reaches the thick one, you will get transmission. In this case the pulse will reflect and be inverted and the transmitted pulse will continue along the thick string w/ no inversion.

If the pulse travels along the thick string, you will get transmission; however, there is no inverted pulse on either side.

[Woozie]

Hmm, I feel like I should know this, but I don't. I'll look through some of my old books later this week when I finally finish my homework.

[Slapper]

Wave starting at light string

[Raen Ryong]

Unless I'm hideously mistaken which is always a possibility,

Edit: Eh, ok. If the incident pulse is traveling along the thin string once it reaches the thick one, you will get transmission. In this case the pulse will reflect and be inverted and the transmitted pulse will continue along the thick string w/ no inversion.

one thing to add to this description is that the amplitude of the wave in the thick string will be less than it was in the thin string. The reflected wave is then a consequence of the conservation of energy.

[Kaylia]

First thought:Yay a physics question, gonna be easy
Second thought: wtf, i dont know


If I understand the question correctly, you're asking how a string would behave if one half was a "big string", and the other half was a "tiny string"?


Sincerely, I'm not sure what the solution would look like, but I know you would have to solve a system of 2 differential equation where the initial condition in the middle are connected y1(x,t) = y2(x,2) to preserve the continuity. and where both section of the string have different linear mass.

Basically,something like this
http://upload.wikimedia.org/math/2/9...5d87161d70.png
with 2 different mu for both section since bigger string should mean larger linear mass.

What the result would be in the end? I've no fucking clue, but the wave would move faster in smaller section to conserve the energy.



http://simplethinking.com/teaching/n...s/image002.jpg
You could make the analogy with a system like this one. If there is a large balls on one end, it would move a lot less. Momentum is going to be conserved similarly in a string.

[Raen Ryong]

Wave speed of the incident wave will be higher in the less dense region as will its wavelength (frequency remains constant).

[Woozie]

First thought:Yay a physics question, gonna be easy
Second thought: wtf, i dont know

Yeah, that's pretty much what I did too lol

[Eliseos]

If I understand the question correctly, you're asking how a string would behave if one half was a "big string", and the other half was a "tiny string"?

I think this is the question being asked, but I'm not sure either. If this is the case, wouldn't the large string have a smaller amplitude than the smaller string?

[Slapper]

I knew I should have just tested this in a lab when I had the chance. The prof was telling us a story about how he and his buddy were arguing about this when they were in grad school and finally went to a lab to test it. Jerk didn't tell us how the end result and decided to put it as a question at the end of the lab report.

The question I'm asking is how the wave traveling along two different strings with different string densities (μ=mass/length of a particular string, each string having a different μ value) would look like; the wave is the same through the entire length of both strings or the amplitude would be different in each string:

http://img192.imageshack.us/img192/3585/string2.png

[Kaylia]

I think this is the question being asked, but I'm not sure either. If this is the case, wouldn't the large string have a smaller amplitude than the smaller string?

To obtain 2 completely different amplitude, the knot would need to remain at y=0 to prevent any discontinuity. It's not impossible at certain frequency, but I don't think it would end up like this all the time.

[Max™]

http://mc2.gulf-pixels.com/wp-conten...ng-Theory1.png

Incidentally, doubling the diameter will halve the frequency on that portion, should give the top result here:

http://img192.imageshack.us/img192/3585/string2.png

http://www.school-for-champions.com/...e_equation.htm

[vivix]

Max is right! woo! zzz

[Slapper]

Thank you kind sir