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)2.5 cm
B)1.7 cm
C)3.4 cm
D)4.2 cm

Question

Quizplus · Accepted Answer

The frequency of a string is inversely proportional to its length. Using the formula $f_1 / f_2 = L_2 / L_1$, where $f_1$ and $f_2$ are the frequencies and $L_1$ and $L_2$ are the lengths, we can solve for $L_2$. Plugging in the given values, $440 / 523 = L_2 / 16$, solving for $L_2$ gives approximately 13.5 cm. The difference between the original length and the new length is $16 - 13.5 = 2.5$ cm.

A Guitar-Like Stringed Instrument Has a String That Is 16