Go Back   Physics Help Forum > College/University Physics Help > Advanced Waves and Sound

Advanced Waves and Sound Advanced Waves and Sound Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Jul 3rd 2015, 08:08 AM   #1
Member
 
kelsiu's Avatar
 
Join Date: Jun 2014
Posts: 67
Question about standing wave

By considering the superposition of two waves propagating through a string, one representing the original or incident wave and the other representing the wave reflected at the fixed end, if both ends of the string is fixed then the waves can reflected and travel back and forth. Standing wave can be formed if the length of the string is an integer numbers of half wavelength.


I just wonder what will we get if the length of the string is NOT an integer numbers of half wavelength and both ends are fixed?
kelsiu is offline   Reply With Quote
Old Jul 3rd 2015, 11:14 AM   #2
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 1,035
What makes you think you can get such a wave to propagate along a stretched string?
studiot is offline   Reply With Quote
Old Jul 3rd 2015, 09:35 PM   #3
Member
 
kelsiu's Avatar
 
Join Date: Jun 2014
Posts: 67
Swing the string with some particular frequency so that the total length of the string is not a integer number of the half-wavelength of the string. When a certain number of waves is transmitted and reflected back and forth we let both ends fixed.
kelsiu is offline   Reply With Quote
Old Jul 4th 2015, 01:37 AM   #4
Junior Member
 
Join Date: Jun 2015
Location: india
Posts: 27
The string will go on vibrating but will be in an irregular manner (will not be uniform like a standing wave) .If a standing wave is prodused on the string each and every point on string will have its on amplitude (ranging from zero to amplitude of the wave that you first created . The end points always have zero amplitude). If it is not a stationary wave ,as you said in your question, the points on string will not have any fixed amplitude but will change their amplitude time to time . So the fiqure you see will be so irregular. I think in most of cases the string will get broken,in practice, since aplitude will not be zero at ends

Last edited by Steve; Jul 4th 2015 at 01:43 AM.
Steve is offline   Reply With Quote
Old Jul 4th 2015, 01:54 AM   #5
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 1,035
Originally Posted by kelsiu View Post
Swing the string with some particular frequency so that the total length of the string is not a integer number of the half-wavelength of the string. When a certain number of waves is transmitted and reflected back and forth we let both ends fixed.
You are beginning to think about it.

If the string is stretched between two fixed points the only way to excite it is to draw it aside in some fashion and then let go ie twang it.
Clearly you cannot waggle the ends since they are fixed.

The only way the string can respond to this is by resonating at its natural frequency or a harmonic, which produces the characteristic standing waves.

If, instead of a single pluck, you physically try to drive the string at some other frequency some of the time the string will be going the same way as your drive and some of the time it will be fighting it, with a net result of no periodic oscillation, just varying movement.


If you only connect one end of the string to a fixed point, the only place you can excite it is at the other end, since you also have to tension it.

Thus your exciter has to be some sort of waving arm since it is not fixed.

You cannot therefore apply a single impulse without reverting to the two fixed point situation.

So you will be continually driving the string.

If your driving action has the same frequency as the string's resonance then again you can excite standing waves, as before.

If not, you will get a time varying response as the ongoing and reflected waves don't match and again you will get a time varying, non periodic response.
studiot is offline   Reply With Quote
Old Jul 4th 2015, 04:34 AM   #6
Member
 
kelsiu's Avatar
 
Join Date: Jun 2014
Posts: 67
I see. Thanks both.
kelsiu is offline   Reply With Quote
Old Jul 4th 2015, 06:20 AM   #7
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 1,035
The end points always have zero amplitude
Nearly but not quite.

It is posiible to generate a standing wave in a heavy string hanging vertically down under its own weight.
In this case the free end will be an antinode.
This is the string version of the organ pipe with one end open.

Otherwise the practical difficulties are as I indicated.
studiot is offline   Reply With Quote
Old Jul 6th 2015, 10:48 PM   #8
Junior Member
 
Join Date: Jun 2015
Location: india
Posts: 27
I was unaware of that one . I was only thinking about a string with both ends fixed and alligned horizondally
Steve is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Advanced Waves and Sound

Tags
question, standing, wave



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
Question about wave functions? muon321 Quantum Physics 1 Jun 6th 2013 02:08 PM
Standing Waves in a Resonance Tube homerbird Waves and Sound 0 Nov 7th 2012 09:23 AM
question about wave equation renlok Waves and Sound 2 Jun 15th 2010 05:51 PM
Question on wave types and a question on fudemetal frequency. George321 Waves and Sound 0 Feb 14th 2010 05:00 PM
Superposition and Standing Waves HELP PLEASE!! JFIII Waves and Sound 2 Feb 26th 2009 08:49 PM


Facebook Twitter Google+ RSS Feed