In a music situation, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. Suppose you have a guitar string playing frequency f0. To increase the frequency upward one octave to 2f0, by what factor should you decrease the length?

Ateacher gives students four liquids commonly found in the kitchen - vinegar, apple juice, dish detergent, and milk - and ph indicator strips, which measure acidity. the teacher asks the students to put the liquids in order from most acidic to most basic. what type of investigation could the students conduct to determine the correct order for the liquids?