A guitar string resonates at 1260 Hz and 1575 Hz with no resonance frequencies in between. Find its fundamental(the lowest) resonance frequency. I know that fundamental frequency is the number of times it completes in one second, measured in hertz. In this specific problem, should I be taking the average of the two given values to calculate the fundamental resonance frequency?
No. The resonant frequencies of a string are integer multiples of the fundamental frequency. The fundamental frequency is somewhere below both of the frequencies listed.
I recall you saying that a few weeks ago when I had a similar problem. My trouble is I do not know how to calculate the fundamental frequency - I know it's an integer, I'm also assuming I don't just pick some arbitrary integer multiple and say that is the fundamental frequency....
You know that the fundamental frequency, multiplied by some number, equals 1260. If the next resonance is at 1575, then you will multiply the resonance by one plus the first number to get 1575.
Calculate the ratio of the frequencies you are given and express that as a fraction. That should give you a hint what the fundamental frequency might be.