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i'm doing a physics experiment. what happens to the frequency if you increase the length of a string?

ok. i'm doing a physics experiment. in this exp. i have two tuning forks and a string. on this string there is a piece of paper. i have to hit the tuning forks, with different lengths of the string and have to notice when the paper on the string vibrates more. any help? i cannot do it in reality because it's only an experimental design!
i ahve to get to know what is the relationship between the frequency and the length

It appears you are doing a standing wave experiment. As the name implies, the wave simply stands in one place (between the two forks) and vibrates up/down (translational).

A wave can exist only within the distance between the two forks (D). And, to be standing, the wave length (L) between the two forks must be some integer multiple (N) of that distance. In math talk, this means D = L/N. As an example, suppose your forks vibrate at a frequency F = k/L; where k is a constant indicating the wave velocity (which depends on a variety of factors like tension, material, etc.).

This means that D = (k/F)/N; where F is the vibrating frequency of your tuning forks and N = 1, 2, 3, .... So you will have constructive interference (and a standing wave) at D = (k/F)/1, (k/F)/2, (k/F)/3,... or, written in terms of L, D = L/1, L/2, L/3, .... For example, if the wavelength of your tuning fork is 2 meters, you'd have a standing wave at D = 2, 1, 2/3, ... distances of the string in meters.

That results because the wave must have constructive interference to exist as a standing wave. That is, all the primary and harmonic frequencies must be additive. Check this out:

"A standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. There is no net propagation of energy." [See source.]

The vibrating fork experiment is an example of a standing wave coming from "two waves traveling in opposite directions." In this case, you have a sort of reflection on the string's vibration off the two forks the string is attached to. That is, you hit the forks, their inherent fundamental waves travel along the string and they meet somewhere along the string. The two forks have to be identifical in frequency for this to work however. And they have to be struck at the same time to simulate the reflected wave.

If the two waves are in synch, there will be constructive interference; otherwise, they will subtract some of their amplitudes and the resulting wave of the string will be minimized. In fact. if the two forks generate like waves, but 180 degrees out of synch so their respective crests cancel each other out, there will be total destructive interference and the string will be absolutely still despite the two forks vibrating.

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