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In a standing wave, how does energy travel past a node?

It should just get reflected. Assume the case of first overtone and you strike the string at a place. How will energy distribute itself?

If it distributes over the whole string, then how is it the wave traveled past a node?

Basically the problem is a standing wave has been set up in the string . Now you strike the string at a place, and this creates a new pulse. Now this pulse will travel past the next node in the string (not the boundary) or will it reflect off even that node and remain confined to a particular region of the string?

Brandon Enright
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2 Answers2

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Waves on strings combine linearly. This means that you can split up a string's motion into two (or more) superimposed waves. The two superimposed waves behave independently, as if the other one was not there. So if you have a standing wave set up on a string, and then you also introduce a travelling pulse, you get something like the following. (The arrows represent the direction of movement, and the node is marked with a blue dot.)

enter image description here

Now to answer your question. I wish I had a way to make the picture animated, but I think you can see it from still pictures. I'm going to draw what happens after a short time, when the pulse reaches the node. The standing wave has also moved, and is now swinging back in the other direction.

enter image description here

As you can see, the standing wave component still passes through zero at the node, as it always must, but the combined wave (pulse + standing wave) does not. Because the pulse and the standing wave do not interact, the pulse just passes straight through the node as if it wasn't there, and the standing wave just keeps waving as if the pulse wasn't there.

Note that not interacting isn't the same as not interfering. Interference happens when two waves get added together and sum to zero, but neither of the two waves is affected by being added in this way, so even when waves interfere, they don't interact.

N. Virgo
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I think you misunderstand the term 'node' in a standing wave.

To help clarify, think of a stringed instrument. If you pluck the string it will resonate at frequency x (with a range of overtones at harmonic frequencies 2x, 3x, 4x etc)

If you push down on the string at the midpoint and pluck at one side of it, you will get frequencies 2x (and its overtones at 4x, 6x, 8x etc) as the part of the string the other side of your finger is stationary.

To show what a node is, just touch the string at the midpoint - very lightly - this will remove the x component completely, leaving you with 2x, 4x etc.) - the difference is that all the odd harmonics (which would have had a maximum at the midpoint) are removed - your finger prevents the midpoint vibrating.

Wikipedia has this lovely graphic on the harmonics page:

enter image description here

The thing to remember is that there is not a reflection at a node - instead, the waves within the string just cancel out at a node. Standing waves are the sum of the actual waves travelling along the string. The energy itself reflects from an end back down the string - which is why you get standing waves.

Rory Alsop
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  • No , I understand what a node means , suppose a standing wave has been set up . and now you strike a tuning fork close to the string –  Apr 28 '13 at 15:06
  • What has the tuning fork got to do with your question? This seems entirely unrelated. So what is ityou are trying to understand? – Rory Alsop Apr 28 '13 at 15:36
  • Suppose one of these waves is set up . And string is vibrating up and down. Now when I strike a string somewhere ,it will create a pulse .does That pulse interferes with the whole string ? or It should remain localised in the specific region between two nodes where it was created ( the pulse ) ? –  Apr 28 '13 at 18:30
  • It travels along the whole string and interferes. The frequencies which fit will remain, the others will be rapidly attenuated. Still not sure what the tuning fork has to do with it though. – Rory Alsop Apr 28 '13 at 18:38
  • How can this new pulse's energy travel through whole string and past nodes ?? And forget about the tuning fork , I was trying to refer to it to create pulse so that when its wave hits the string , string vibrates . but now i plucked the string . –  Apr 29 '13 at 04:46
  • @nonagon You can think of the node as still having torque. Even though it isn't moving up and down the wave peaks around it move up and down and that obviously has a twisting effect at the node. – Brandon Enright Apr 30 '13 at 04:38
  • @BrandonEnright Please explain this then , the first part of the string wave . http://skullsinthestars.com/2010/04/07/wave-interference-where-does-the-energy-go/ , I think he means to say , that energy can't travel past node , but how it travels is explained using a mathematical trick called interference , and this trick tells us how energy will redistribute itself and here in this case , (trick)it'll be something that cancels the new pulse created everywhere else except the region where I created it to predict the correct redistribution of energy . –  Apr 30 '13 at 04:42
  • Remembering my laser optics course at university twenty-something years ago, I would say that skullsinthestars website has a lot of bad physics. Energy does travel past nodes, diffraction is not how dvd players work etc. – Rory Alsop Apr 30 '13 at 05:43
  • His explanation for light wave interference seems correct as they are ultimately photons and qmechanics . But the trouble I am facing is understanding about interference of wave on a string. –  Apr 30 '13 at 07:35
  • Key thing is - energy does travel past nodes. Once you understand that, the rest is easy. See Brandon's comment above. – Rory Alsop Apr 30 '13 at 09:36