Okay I usually don't post on here I just come on to read, but I have a huge physics lab due tomorrow and can't figure out the last question. Everyone on here seems pretty smart so if anyone is good at physics maybe they can help me out. The question is how does the density of the material making up a wire and the length of the wire affect the frequency? If anyone can help me with this I'd be very grateful. If not well I guess I'll keep searching for an answer that I understand. Posted by El JT de Spang (Member # 7742) on :
What you need to do is search through your lab for an equation that has both density and frequency. Or any variables that get you to density and frequency (such as mass or wavelength). Then, once you've got frequency, density, and length into an equation you see what happens if you hold one constant and increase the other. If they both go up together, they have a proportional relationship. If one goes down while the other goes up then they have an inverse relationship.
Yes, I know the answer, and no, I won't just tell you.
Posted by Bob_Scopatz (Member # 1227) on :
Think of two guitar strings, one nylon, one steel.
They are clearly of different densities.
If you tune them to the same pitch...
They'll have different tonal qualities, to be sure. But are they vibrating at the same frequency -- that's the question...
That's not a direct or complete answer to your question, but I hope it sets you on the right track.
Edit to add...
Also...know that sound travels faster in dense material than in less dense material. So, speed of travel down the wire string versus the plastic one...
Also...google is your friend.
[ February 14, 2006, 10:28 PM: Message edited by: Bob_Scopatz ]
Posted by lildipper101 (Member # 8860) on :
lol thanks and EL JT de Spang I didn't expect you to just tell me but there are no equations in the lab that deal with density and its affects on frequency or length. If there were I wouldn't have this problem. The lab was about tension and its effects on frequency. Wait could you consider density and diameter in a sense to be close to the same thing because the bigger the diameter the string is wouldn't it be more dense?
Posted by King of Men (Member # 6684) on :
Frequency of what? Also, if it's a lab, you should have been measuring this at some point; check your results to see if you measured frequencies for different lengths and densities.
Posted by El JT de Spang (Member # 7742) on :
No. Diameter has no effect on density. Density is mass over volume. Increasing diameter increases them both proportionally.
Think of water. A glass of water has the same density as a pond of water, since density is unitless.
Posted by King of Men (Member # 6684) on :
It depends on the definition of 'density'. Is it defined as 'mass / length', which is sometimes used in problems involving strings? (I think there is some particular name for this; it's been a long time since I did any tension problems.) Or is it the usual definition, mass / volume? Because if so, you are way off base.
Posted by Bob_Scopatz (Member # 1227) on :
KoM...are you thinking of "linear density of a string?" That's mass per unit length.
Posted by King of Men (Member # 6684) on :
Ah, that was it, yes. Posted by lildipper101 (Member # 8860) on :
OK the problem is we didnt' actually do the lab just got the results to interpret. lol and right now google is killing me. I keep getting onto web pages way to complex for the level of physics I'm at. I know there's a proportionality statement for density and frequency but I can't remember what it is. I think it might be something like f=1/square root d. But I'm not sure.
Posted by lildipper101 (Member # 8860) on :
lol I think I'm just gonna go find a piece of long string and see what happens when I try and make waves at different lengths that should help me out with the length part at least. For density I think from what I've read that the greater the density the lower the frequency. I think or I've got it backward. Because wouldn't it be harder for waves to travel through a denser material?
Posted by Dagonee (Member # 5818) on :
The following is speculation, not to be relied on for homework. Corrections welcome.
Here's my thinking on it, no googling:
1.) Increased density means more mass per linear unit.
2.) This means a denser string requires more energy to accelerate a given linear unit.
3.) This suggests that the speed of the wave in a denser string will be slower than the speed of a less dense string.
4.) Slower speed = lower frequency.
Edit: BTW, the length is trivial to determine: just pick up a guitar or a banjo and play it a little while.
Posted by El JT de Spang (Member # 7742) on :
quote:Because wouldn't it be harder for waves to travel through a denser material?
Do some simple checking at your dorm/house/apt on this. Check water, air, and wood with sound waves and see which does the best job conducting sound waves.
Posted by lildipper101 (Member # 8860) on :
Okay thanks everybody! I"m going to go try some of this stuff out, because I think that'll be the best way to understand it, but everyone has been a great help. Thanks!
Posted by rivka (Member # 4859) on :
quote:Originally posted by El JT de Spang: density is unitless.
Really? That's news to me.
Posted by Bob the Lawyer (Member # 3278) on :
Perhaps he meant specific gravity?
Posted by rivka (Member # 4859) on :
Oh! That could be.
Thanks, Bob. Posted by HollowEarth (Member # 2586) on :
quote:Originally posted by rivka:
quote:Originally posted by El JT de Spang: density is unitless.
Really? That's news to me.
He meant its an intensive quantity. Although those are not the words he wrote.
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