Two interesting problems.

[jrd007]

I was reading over my Physics book during break, what a shock huh, during my break? lol. Well I ran across two questions that interested me, they are not homework problem but I was curious about them. So I thought I would see if anyone knew the answers. So here they are.

1) Why are the frets on a guitar spaced closer together as you move up the fingerboard toward the bridge?

and...

2) Explain how a tube may be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)

[berkeman]

for 1, how are the musical notes spaced in frequency? They're not a linear progression, are they?

for 2, the first part of the question reminds me of a pipe organ with the different notes resonating at different pipe lengths, but the second part of the question with the muffler example involves more of the quieting effect of the packing, I would think. In performance exhausts, you tune the lengths and sizes of various parts of the exhaust system to maximize scavanging and other effects, nothing to do with the exhaust sound. Then you muffle as much as you need to with packing to meet external sound requirements.....

[Tide]

Also, the fundamental frequency of a vibrating string does not vary linearly with its length.

[jrd007]

So why are they closer together as you movie up? No one's knows?

[Orefa]

So why are they closer together as you movie up? No one's knows?
I know! It's because of how the musical notes are spaced in frequency. They are not a linear progression, the fundamental frequency of a vibrating string does not vary linearly with its length.

...I'm sooo smart. :biggrin:

[jrd007]

So the answer ro # 2 is that basically you get to tune the lengths and sizes of such filters and then pack it to get different sounds?

[berkeman]

So why are they closer together as you movie up? No one's knows?
I googled physics of guitar strings, and this hit looks like it should be interesting:

http://ffden-2.phys.uaf.edu/211.web.stuff/billington/main.htm

[jrd007]

So the answer to # 2 is that basically you get to tune the lengths and sizes of such filters and then pack it to get different sounds?

[berkeman]

So the answer to # 2 is that basically you get to tune the lengths and sizes of such filters and then pack it to get different sounds?
I honestly don't know what the answer to #2 is. I've never heard of a muffler as being a tuned device before, I just assumed it was the packing material that did the quieting of the noise.

The only possibility that I can think of is if maybe the length of the muffler is tuned to match the worst noise frequencies, so that the energy in those frequencies tries to resonate in the muffler. And maybe that causes more loss at those frequencies, since the air molecules will be moving faster due to the resonance, which may cause more loss in the packing material....? But that's a bit of a stretch. Sorry I'm not of much help on that one.

[Orefa]

If the length of the tube matched the wavelength of an incoming sound, wouldn't it bounces back out and cancel out the incoming wave?

I think mufflers work mainly by reflecting sound waves in such a way that they cancel each other out.

[berkeman]

Silly me. Howstuffworks.com has a long writeup on mufflers and noise cancellation. Doh! I should have checked there earlier:

http://auto.howstuffworks.com/muffler.htm

[jrd007]

Thank you!