A guitar string is `180 cm` long and has a fundamental frequency of `90 Hz`. Where should it be pressed to produce a fundamental frequency of `135 Hz`?

Answer

`120 cm` from on end.

Explanation

`f = (1)/(2L) sqrt((F)/(mu))`
as `F` and `mu` are fixed
`(f_(1))/(f_(2)) = (L_(2))/(L_(1))`
`L_(2) = (f_(1))/(f_(2)) L_(1) = (90)/(135) xx 180cm = 120 cm`
thus the string should be present at `120 cm` from an end