On Laws of vibrating string

1. Jun 26, 2004

franz32

Hello, I need help or guidance.

1. What are the laws of vibrating string? Does it have something to do with
f = (1 / 2L) (T / u)^1/2 where f is frequency, T is tension and u is mass per unit length of the string?

2. What method can I use to determine if the string has the same frequency as the tuning fork? (Well I know that one method is by the sense of hearing)

3. To determine the linear mass density, will I divide my mass of the string to the length of the string? Oh, what "exactly" does linear mass density mean?

4. If the string is vibrating with its fundamental frequency , how is wavelength of the sound produced related to the length of string? Is it directly proportional bec. wavelngth = 2 X Length..?

5. If I would like to find the fundamental frequency of a vibrating string, will I use the formula written on question # 1?

2. Jun 26, 2004

HallsofIvy

Staff Emeritus
What do you mean by the "laws" of vibrating string? Once you know the frequency, vibration is vibration and has the same laws!

Yes, the fundamental frequency of a string of density u, length L, and tension t is given by f= (1 / 2L) (T / u)1/2 so the answer to (5) is "YES".

2) Given what? Given such things as u, T, L, you could calculate f and see if it is the same. Not given that, by ear! Oh, wait, from my shiftless days playing the guitar (badly): hold the tuning fork close to the string, hit the tuning fork to get a note and then feel the string to see if it vibrates "sympathetically". If so, they have the same frequency.
That's the standard method of tuning a stringed instrument.

3) Yes, of course: mass divide by length is exactly what mass PER unit length means!

4) The "fundamental wavelength" IS, by definition, the lowest frequency, hence longest wavelength possible. That is precisely twice the length of the string since we have to have the "nodes" at the points where the string is fastened.,