Standing waves on a string

Your job today is to predict the frequencies required to set up standing waves on one (or two) strings, and compare those predictions to reality in an experiment. You must hand in a report which addresses all the items below, with any graphs, pictures, and calculations required. Staple your report pages together and place them in your folder before you leave. Neatness counts.

Warnings:

• Do not increase the amplifier's volume beyond mark 4 out of 10
• Do not allow the amplitude of the oscillator to exceed 0.5 cm
• The sound of the vibrator should barely be audible -- if you hear knocking or tapping sounds, call me over at once!

Using elastic cord ....

First, measure some properties of the elastic cord. You'll need to include uncertainties in just about every quantity.

1. Hang the mass by the cord over the pulley. Place tiny marks on your cord at the location of the vibrator and the pulley.
2. Measure the distance between the marks on your cord when the cord is unstretched, and when it is stretched between vibrator and pulley with 750 g hanging from it.
3. You can find several pieces of cord on the table at the middle of the room. Determine the linear mass density of unstretched cord using one or more of those pieces.
4. Compute the linear mass density of your cord when it is stretched and holding 750 g. Include an uncertainty.
5. You should now be able to compute the speed of waves travelling down the stretched cord, and an uncertainty in that speed.
6. Predict the four lowest frequencies (with uncertainties) which should yield standing waves on the stretched string. Draw pictures of each wave.

Stop and show your work to an instructor. When he approves, continue.

1. Using the function generator and amplifier, measure the actual frequencies which yield the four waves you predicted above. Include an uncertainty.
2. Do your predictions agree with the actual frequencies, within their mutual uncertainties?

If you find a systematic difference, call the instructor over to discuss it. There may be an explanation ...

If you have time, turn the page over ....

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Using fishing line ....

Now, let's repeat the experiment with a very different type of string. The fishing line is (for our purposes) a fixed length under any tension. But since the fishing line is much lighter than the cord, we'll change the hanging weight so that its mass is 200 g.

1. Cut a piece of fishing line long enough to replace the elastic cord. Measure its mass and unstretched length. Compute its linear mass density, and the uncertainty therein.
2. Assume that the stretched mass density of the line is the same as its unstretched mass density.
3. Compute the speed of waves travelling down the fishing line when it supports a 200 g weight, and an uncertainty in that speed.
4. Predict the four lowest frequencies (with uncertainties) which should yield standing waves on the fishing line. Again, draw pictures of each wave.

Stop and show your work to an instructor. When he approves, continue.

1. Leave the elastic cord attached to your aluminum rod! Slide the other end of the cord off the hanging weights.
2. Tie one end of the fishing line to the rod (above the cord), and the other end to the weights.
3. Using the function generator and amplifier, measure the actual frequencies which yield the four waves you predicted above. Include an uncertainty.
4. Do your predictions agree with the actual frequencies, within their mutual uncertainties?

If you find a systematic difference, call the instructor over to discuss it. There may be an explanation ...

If you have more time ...

• Set up a standing wave with 10 nodes in the elastic cord. How close is the actual frequency to the predicted frequency?