Question

increase your frequency until you get a new standing wave. what frequency does this occur?
based on setup_________
what relationship are you discovering between the frequencies? _________ develop
a hypothesis and test it.
i think
____________________

Explanation:

This problem relates to standing waves, which is a concept in Physics (a subfield of Natural Science). Standing waves in a string or air column have harmonic frequencies. The new standing wave frequency (for a string fixed at both ends, e.g.) occurs at integer multiples of the fundamental frequency ($f_n = nf_1$, $n = 1,2,3...$). The relationship is that successive standing wave frequencies are integer multiples (harmonics) of the lowest (fundamental) frequency. A hypothesis could be "Standing wave frequencies are integer multiples of the fundamental frequency", tested by measuring frequencies for different harmonics and checking the ratio.

Answer:

For a typical standing - wave setup (e.g., string fixed at both ends), the new standing - wave frequency occurs at an integer multiple of the fundamental frequency. The relationship between the frequencies is that the frequencies of standing waves are harmonic (integer multiples) of the fundamental frequency. A hypothesis could be: "The frequency of each subsequent standing wave is an integer multiple of the fundamental standing - wave frequency." To test it, one can measure the frequency of the fundamental standing wave ($f_1$) and then measure the frequencies of the next few standing waves ($f_2,f_3,\cdots$) and check if $f_n=nf_1$ (where $n = 2,3,\cdots$) holds.