# Resonance of a Stretched String

1. Sep 21, 2016

### Taniaz

1. The problem statement, all variables and given/known data
This is actually a lab experiment which includes a stretched string which is clamped to one end with a G-clamp and the other end with a pulley and some masses hung from it. There's a bar magnet placed underneath the string near the pulley and a movable bridge to alter the length of the string. It's connected to an AC supply and a rheostat.

2. Relevant equations
L= lambda / 2 but I don't know what lambda is.

3. The attempt at a solution
I've connected everything together but I get no vibration at all. Pictures attached below. Any help at all will be seriously appreciated!

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2. Sep 21, 2016

### TSny

You will get a stronger magnetic field at the wire if you place one of the poles of the magnet near the wire (instead of having the center of the magnet near the wire). Better would be to use two magnets so that the wire is between the N pole of one magnet and the S pole of the other magnet, with just a small gap between the poles.

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3. Sep 21, 2016

### Taniaz

Two magnets placed together with the wire between them? But then the opposite poles would stick to one another crushing the wire in between or do I place the magnets underneath the wire?

What about the movable bridge? What material should it be made up of? Since we don't have one, we have to improvise. Are there any specifications for the distance between the magnets and the movable bridge? How does adding weights affect the vibration (is it like guitar string tuning? when you add weight you're actually changing the frequency of the note?)

And the AC supply? I need it to be at 50 Hz so should I just leave it at 2V or change it?

Thank you.

4. Sep 21, 2016

### Taniaz

Or did you mean one magnet near the pulley and the other near the G-clamp with the movable bridge in between?

5. Sep 21, 2016

### TSny

Right. You will need to keep the magnets from pulling together. Start by just holding the magnets to keep a small gap between the N pole of one magnet and the S pole pole of the other magnet. The wire string will pass through the gap. You can try putting the gap between the magnets at different places along the string.

I'm guessing the purpose of the bridge is to support one end of the wire string. Moving the bridge to different positions allows you to adjust the length of the vibrating section of the wire. The material of the bridge should not matter as long as it supports the wire at one point.
Yes, adding weights changes the tension in the string. If you are trying to get the fundamental mode of vibration (L = λ/2), then it might require quite a bit of tension. This could require a large amount of weight on the weight hanger. I would try to get one of the higher modes of vibration first. At first, you can have someone pull down on the weight hanger with varying force to gradually change the tension until you find the right tension to produce one of the standing wave modes.

You want to to get maximum current without overheating the wire. I don't know if 2V is sufficient.

Of course, you want to make sure you have good electrical connections. If the wire has an enamel coating, then you need to scrape off the enamel at the electrical contact points.

6. Sep 21, 2016

### Taniaz

The bar magnets that I have are really strong and they just stick together even if I put them a small distance apart. If I do that then that will restrict the wire movement?
What if I use one bar magnet around the wire? Will that be sufficient?

I don't understand this part: "You can try putting the gap between the magnets at different places along the string."

The length of the wire will be the distance from the movable bridge to the centre of the pulley?

Since we don't have any plug-croc leads as of yet, I've actually tied the normal lead with a copper wire to the part of the wire on the pulley to complete my circuit as shown in this picture? Will this pose a problem?

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7. Sep 21, 2016

### TSny

When I would do this demonstration in class, I used a strong electromagnet instead of bar magnets. The poles of the electromagnet were rigidly held in place. You can try just one magnet. I don't know if the field will be strong enough.

Two different locations of the magnets are shown in the overhead view below. You can try other locations.

Yes.

I'm not quite following what you are saying here. As long as you are getting a large current through the section of wire between the pulley and the bridge, you should be OK. Can you tell if you are getting any current? The wire should become warm after just 15 seconds or so.

8. Sep 21, 2016

### Taniaz

I tried placing them close to one another but the wire got caught in between and snapped. Will a U-shaped magnet not work better than the bar magnets I have? We don't have electromagnets I'm afraid.
The copper wire should lie in between the opposite poles of the bar magnets, not above or below it right?

I meant to say that since we didn't have leads with crocodile clips I couldn't clip the leads onto the wire to complete the circuit. So I just tied the leads around the wire using some more copper wire if that makes sense. I'm afraid that might mess up the electrical contact bit you were mentioning. I'm not in the lab at the moment so I'll have to check and see if it gets warm because it wasn't when I was doing it earlier. I could feel a slight vibration but I couldn't see anything.

Also, I've got 100 g slotted masses and the total length of the copper wire being used is 150 cm. How many masses do you recommend putting at first?

9. Sep 21, 2016

### TSny

Wow, strong magnets. I would try using just one magnet with one of the the poles a few millimeters from the wire (just imagine removing one of the magnets in my picture above).
I don't think a U-shaped magnet would work any better because the two poles of the U-shaped magnet are relatively far apart. But certainly give it a try!
Yes. You are trying to get the strongest possible magnetic field directed perpendicular to the wire.

OK

Feeling a vibration is promising!

I would not use any slotted masses at first. Using one hand, I would gently pull down on the weight hanger to slowly and continuously increase the tension until one of the possible standing waves is produced. The tension has to be "just right" to get a good standing wave.

10. Sep 21, 2016

### Taniaz

Thank you for your help. I'll be in the lab again tomorrow, so I'll let you know if I get anything at all!

11. Sep 21, 2016

### Taniaz

The maximum voltage on the power supply I have is 12 V. Is that sufficient?

12. Sep 21, 2016

### TSny

I would think so, but I can't say for sure. If you are not getting enough current, then make sure the rheostat is set at minimum resistance. In the picture below, it looks like it's set at maximum resistance.

13. Sep 22, 2016

### Taniaz

So I removed the rheostat completely but I'm still getting nothing. I found two less stronger magnets than the previous ones and I've set them at a small distance apart but still nothing :/

14. Sep 22, 2016

### Taniaz

No current seems to be passing through the circuit. The power supply is working because I connected it to a separate circuit with a light bulb and it works. We also tried this light bulb circuit with just the copper wire we're using and then it doesn't light. So it something wrong with the copper wire?

15. Sep 22, 2016

### TSny

Does the copper wire have an enamel coating? If so, then you need to scrape off the coating at the places where you connect the wire to other parts of the circuit.

16. Sep 22, 2016

### Taniaz

Hi thank you for replying. Ok so that's a good idea and I really hope it works. Most recent pictures attached, the magnets have been positioned as you told me to. Can you take a look at how we've connected the lead to the copper wire?

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17. Sep 22, 2016

### TSny

The circuit looks correct to me. You just want to make sure you have good connections at the locations shown below. The metal parts of the plugs need to make good contact with the bare copper wire.

Also, I think you will need quite a bit more distance between the pulley and the bridge, maybe a couple of meters.
It would help to get the poles of the magnets closer to the wire, but I know you are having trouble with the magnets pulling together.

18. Sep 22, 2016

### Taniaz

Yes this is what I was trying to say yesterday because we don't have wires with crocodile clips we have to improvise. How can we ensure good electrical wire without crocodile clips?
We actually have two setups. The length of the wire in this setup from the centre of the pulley to the wire held beneath the G-clamp is 1 m and the copper wire is slightly thicker.
The previous setup had a copper wire of length 1.5 m and it was slightly thinner.

19. Sep 22, 2016

### TSny

I would tightly wrap the wire several times around the metal part of the plug in the picture below. If there is an enamel coating on the wire, then make sure you scratch off the enamel (using sandpaper if possible) on the wire where it wraps around the plug.

The important length is the distance between the bridge and the pulley since that's the section that will be vibrating. One to two meters should work. Try different lengths.

20. Sep 22, 2016

### Taniaz

Alright, I'll try this soon. I might not find sand paper but I saw that we can use nail files or a thin knife as well?
I was just wondering, why does it not work with the enamel? I was thinking about the sonometer wires, do they have an enamel around them?

As for the lead attached to the pulley, I'll have to do the same? Only scrape off the area it's in contact with right?