1. The problem statement, all variables and given/known data Predict the effect temperature will have on the frequency of the string (considering your results and your knowledge of science). Explain and back up your hypothesis 2. Relevant equations http://img166.imageshack.us/img166/2544/lvsfie2.jpg 3. The attempt at a solution Nothing so far. I'm clueless.
What happens to a solid as you heat it? Think of the graphs that you have provided because they will come in handy when you know what happens to heated solids.
The molecules move faster. So, if you increase the temperature, the frequency will increase? Where do the graphs tie into this?
No. Think of it in a bit more detail. Say you have a string of length L fixed at both ends. You pluck the string, and you get a fundamental tone of some frequency. Now for clarity, remove the string from the end clamps and heat it up. What happens to the length of string as it is heated? Now that it is heated, keep it at that temperature and put it back into the clamps that are spaced L apart. What can you say about the string tension now?
Ok, so, if you heat up the string, it becomes bigger (longer) - tension decreases. According to the graphs, when the length is increased, the frequency decreases. Same with tension. Is that right? If yes, where should I start to figure out the actual relationship?
The question just asks you to predict so you need not know the exact relationship. State what happens to the string when its heated and what happens to the frequency due to that or those particular parameters being changed.
Does the wave length of the sound change is the temperature is increased? If not, when the temperature increases, doesn't the speed of sound increase? Which using the universal wave equation v = f x lamba, the frequency would increase in order to have the speed increase? Not sure, if there is anything else I am not taking into account.
Yes, the speed of sound in air increases with temperature, but that's not relevant here. The frequency is fixed by the vibration of the string, not the air. The wavelength of the sound in the air is not the same as the length of the string! Think what happens to a guitar string when you change the frequency by changing the tension (by turning the the tuning peg) and the length is constant. In the string, the wave speed is changes and the wavelength is constant. In the air, the wave speed is constant and the wavelength changes.