Question

the ratio of the lengths of strings that play the notes F and G is 9 to 8. If a string 88 centimeters long plays a G, what is the lenght of the string thst plausan F?

Answer 1

48/8=6

6*9=F

54=F

Hope this helps

Answer 2

9/8 = 1.125 is called a "just" major second. Just tuning means each interval in a fixed key is tuned as consonant as possible, to small whole number ratios.

In modern music we change keys all the time, and equal temperament is used. That means each frequency or length is related to the previous semitone by a factor of
`\sqrt[12]{2}`, the 12th root of 2. So a tempered major second is
`2^(\frac 1 6) \approx 1.1224`, about four cents flat compared to a just second.

That doesn't matter to the problem, but I have to do something to keep these straightforward ones interesting.

f/g = 9/8

f = (9/8) g = (9/8) 88 cm = 99 cm

Answer: 99 cm