Why do different pipes/strings make different sounds?

[donkeycopter]

Hi,

We're doing wave theory in class, so we've done stuff like open/closed pipes, universal wave equation etc.

I can't understand why different sounds are made in different length pipes or strings however! I mean for example in a closed pipe, the length is always a quarter of the wavelength right? So if that is always the same, how are different sounds produced? Likewise in strings.

Thanks!

 

[collinsmark]

Is this an actual homework question or are you just curious?

 

[donkeycopter]

Is this an actual homework question or are you just curious?

does it matter?

 

[collinsmark]

Well, yeah sort of. Your answer determines how much explanation I can give you.

 

[collinsmark]

Okay, I'll assume this might be for homework, so I'll just try to point you in the right direction.

In a closed pipe, the fundamental wavelength is always 4 times the length of the pipe. But there can still be "harmonics." What are harmonics? Well, that's what you'll have to research for your homework. Doing an Internet search on "harmonics" and "standing waves" might be a good start.

But just to spark your curiosity: (Without explaining what harmonics are [that's for you to find out], I'll try to give you an idea why they matter.)

Harmonics are how bugles work.

If you have a guitar available, try this. With your left hand, lightly touch a string just above the 12 fret as you pluck the string. The immediately release your left-hand finger. You'll hear a note one octave higher than if you didn't touch the string with your left hand. Now do the same thing except touch just above the 7th fret. You'll get a higher note, Now try the 5th fret. That's 2 octaves up. Even the 4th and 3rd fret positions have harmonics.

If you interested in why different instruments (different types of pipes, strings, etc) sound differently even when playing the same note, it involves these harmonics. (But I'll let you research how for yourself.) Suffice it to say, harmonics shape the tone of the instrument.

Harmonics are not only used in music, but many aspects of physics and mathematics, such as the mathematics of Fourier transforms and [Fourier] series coefficients. Understanding harmonics is a substantial part of communication theory such as how cell phones and wireless networks work (and even wired communications such as USB, LAN connection, etc. to some extent), radios, TV, and many other high-tech things (and some low-tech too!).

Going even deeper, a little more than a century ago, a man named Max Planck was doing some research involving the spectrum of things that emit light because they are really hot. He came up with a model using these principles of standing waves and their harmonics. This model opened the door -- opened the 'rabbit hole', if you will -- to what we now call quantum mechanics. The world of physics has never been the same since.

 

[donkeycopter]

Actually, it isn't a homework question, it would be a pretty horribly worded question if it was! :) I'm just trying to get a better understanding of the concept.

Thanks for the response, but I don't see how it answers my question?

 

[collinsmark]

Actually, it isn't a homework question, it would be a pretty horribly worded question if it was! :) I'm just trying to get a better understanding of the concept.

Thanks for the response, but I don't see how it answers my question?

Again, and Internet search using the keywords:

+"standing waves" +harmonics +music

should answer your questions. For example, here is a link that came up near the top when I did the search.

http://cnx.org/content/m12413/latest/"

It seems pretty informative.

Essentially, dividing the fundamental wavelength by an integer gives you the wavelength of another "valid" standing wave. These higher order harmonics can exist (as standing waves) for the same reason the fundamental wavelength can exist as a standing wave. It's all about integers.