This preview shows page 1-2-3-27-28-29 out of 29 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 29 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

189 189189 1891812010-05-03 18:56:53 / rev 4d10a37f52ad+9.2 Musical tones9.2.1 Wood blocksHere is a home musical experiment that illustrates proportional reasoningand springs. First construct, or ask a carpenter or a local lumber yard toconstruct, two wood blocks made from the same larger wood plank. Minehave these dimensions:1. 30 cm × 5 cm ×1cm; and2. 30 cm × 5 cm ×2cm.The blocks are identical except in their thickness: 2 cm vs 1 cm.Now tap the thin block at the center while holding it lightlytoward the edge, and listen to the musical note. If you do thesame experiment to the thick block, will the pitch (fundamentalfrequency) be higher than, the same as, or lower than the pitchwhen you tapped the thin block?You can answer this question in many ways. The first is to dothe experiment. It would be nice either to predict the resultbefore doing the experiment or to explain and understand theresult after doing the experiment.One argument is that the block is a resonant object, and the wavelengthof the sound depends on the thickness of the block. In that picture, thethick block should have the longer wavelength and therefore the lowerfrequency. A counterargument, based on a different model of how thesound is made, is that the thick block is stiffer, so it vibrates faster. On theother hand, the thick block is more massive, so it vibrates more slowly.Perhaps these two effects – greater stiffness but greater mass – cancel eachother, leaving the frequency unchanged?I’ll do the experiment right now and tell you the result. The thick blockhas a higher pitch. So the resonant-cavity model is probably wrong.Instead, the stiffness probably more than overcomes the mass.A spring model explains this result and even predicts the frequency ratio.In the spring model, a wood block is made of wood atoms connected by189 189189 1891812010-05-03 18:56:53 / rev 4d10a37f52ad+9.2 Musical tones9.2.1 Wood blocksHere is a home musical experiment that illustrates proportional reasoningand springs. First construct, or ask a carpenter or a local lumber yard toconstruct, two wood blocks made from the same larger wood plank. Minehave these dimensions:1. 30 cm × 5 cm ×1cm; and2. 30 cm × 5 cm ×2cm.The blocks are identical except in their thickness: 2 cm vs 1 cm.Now tap the thin block at the center while holding it lightlytoward the edge, and listen to the musical note. If you do thesame experiment to the thick block, will the pitch (fundamentalfrequency) be higher than, the same as, or lower than the pitchwhen you tapped the thin block?You can answer this question in many ways. The first is to dothe experiment. It would be nice either to predict the resultbefore doing the experiment or to explain and understand theresult after doing the experiment.One argument is that the block is a resonant object, and the wavelengthof the sound depends on the thickness of the block. In that picture, thethick block should have the longer wavelength and therefore the lowerfrequency. A counterargument, based on a different model of how thesound is made, is that the thick block is stiffer, so it vibrates faster. On theother hand, the thick block is more massive, so it vibrates more slowly.Perhaps these two effects – greater stiffness but greater mass – cancel eachother, leaving the frequency unchanged?I’ll do the experiment right now and tell you the result. The thick blockhas a higher pitch. So the resonant-cavity model is probably wrong.Instead, the stiffness probably more than overcomes the mass.A spring model explains this result and even predicts the frequency ratio.In the spring model, a wood block is made of wood atoms connected byComments on page 1 1Comments on page 1I feel like you covered a variety of examples and this is the first time involving music. Iam quite happy.For Wednesday (memo due at 9am on Wed), read about the wood-block demonstrationfrom lecture. Then we’ll talk more about physics and music (provided I’m not in thedelivery room at Mt Auburn hospital).I like this introduction. It seems abstract, but you know it is building up to a meaningfulconclusionThis was a cool example to see in class! I really like how the readings tie to the lectures,but I also think even for people who don’t take 6.055 (which will probably be the casefor most readers of this text), that the examples are so interesting to read about and theexplanations are very clear.I know, I’m ashamed I couldn’t remember the results of this from streetfighting math..I like the idea of using springs as music, but the more classical idea of springs. I wonderhow that would work...not just vibrational motion but like a slinkyI see that this could be a good way to make the point, but do you really expect anyone tohave a carpenter or lumber yard worker make this for them?I realy don’t think that’s relevant...Haha yeah pretty irrelevantAlso, it’s not really construction. Most places will happily cut down lumber foryou.Rather than instructing the reader in how to acquire the wood blocks youcould simply ask them to acquire blocks - if you’re target audience is MITstudents I would assume they are capable of figuring out a way to get twowood blocks.I also assume that this statement applies to the average person as well!189 189189 1891812010-05-03 18:56:53 / rev 4d10a37f52ad+9.2 Musical tones9.2.1 Wood blocksHere is a home musical experiment that illustrates proportional reasoningand springs. First construct, or ask a carpenter or a local lumber yard toconstruct, two wood blocks made from the same larger wood plank. Minehave these dimensions:1. 30 cm × 5 cm ×1cm; and2. 30 cm × 5 cm ×2cm.The blocks are identical except in their thickness: 2 cm vs 1 cm.Now tap the thin block at the center while holding it lightlytoward the edge, and listen to the musical note. If you do thesame experiment to the thick block, will the pitch (fundamentalfrequency) be higher than, the same as, or lower than the pitchwhen you tapped the thin block?You can answer this question in many ways. The first is to dothe experiment. It would be nice either to predict the resultbefore doing the experiment or to explain and understand theresult after doing the experiment.One argument is that the block is a resonant object, and the wavelengthof the sound depends on the thickness of the block. In that picture, thethick block should have the longer wavelength and therefore the lowerfrequency. A counterargument, based on a different model of how thesound is


View Full Document

MIT 6 055J - Lecture Notes

Download Lecture Notes
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture Notes and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture Notes 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?