A guitar-like stringed instrument has a string that is 16 cm long. It sounds the musical note A(440 Hz) when played without fingering. By what distance should you shorten it to play the note C (523 Hz)?
A) 3.4 cm
B) 2.5 cm
C) 4.2 cm
D) 1.7 cm

Question

A guitar-like stringed instrument has a string that is  16 cm long. It sounds the musical note  A(440 Hz) when played without fingering. By what distance should you shorten it to play the note C (523 Hz)?
A)  3.4 cm
B)  2.5 cm
C)  4.2 cm
D)  1.7 cm

Quizplus · Accepted Answer

The frequency of a string is inversely proportional to its length. To find the new length for 523 Hz, use the ratio 440/523 = L/16. Solving for L gives approximately 13.5 cm. The string should be shortened by 16 - 13.5 = 2.5 cm.

A Guitar-Like Stringed Instrument Has a String That Is