Chapter 2: Q17DQ (page 497)
A musical interval of an octave corresponds to a factor of 2 in frequency. By what factor must the tension in a guitar or violin string be increased to raise its pitch one octave? To raise it two octaves? Explain your reasoning. Is there any danger in attempting these changes in pitch?
Short Answer
To raise its pitch one octave the tension in a guitar or violin string be increased by factor 4 and to increase by two octaves then increase the tension in the string by factor 16.