A guitar-like stringed instrument has a string that is 20 cm long.It sounds the musical note A (440 Hz)when played without fingering.How far from the end of the string should you place your finger to play the note C (523 Hz)?
A)3.2 cm
B)2.1 cm
C)4.2 cm
D)5.2 cm

Question

Quizplus · Accepted Answer

The correct answer is A.The frequency of a string is inversely proportional to its length. So, to play a higher note (higher frequency), you need to shorten the string. To play the note C (523 Hz), which is higher than A (440 Hz), you need to shorten the string by a factor of 440/523 = 0.841. So, the new length of the string should be 20 cm * 0.841 = 16.82 cm. To find how far from the end of the string you should place your finger, you need to subtract the new length from the original length: 20 cm - 16.82 cm = 3.18 cm. So, you should place your finger 3.18 cm from the end of the string to play the note C.

A Guitar-Like Stringed Instrument Has a String That Is 20