I have a question about the wave of the string. Please help!!?

Question

A violin string has the standard length of 32.8cm. It sounds the musical note A (f1 = 440Hz) when played without fingering. How far from the end of the string should you place your fingers to play the note C (f2 = 523Hz)?

From the f1, f1=v/2L, solve for v, v=2(0.328m)(440Hz)=288.64 m/s. Now f2=2v/2L=523Hz, solve for L, L=(288.64m/s)/(523Hz)=0.552m. This 0.552m is longer than the standard length of 0.328m, then, where should I put my fingers to shorten the length in order to have 523Hz? is it supposed to be shorter than the standard length? Am I missing something or am I totally misunderstood the question? Please help me!!!

Thanks.

Answer 1

why did you use f2=2v/2L when solving f2?  If you use f2=v/2L, you would get the length corresponding to 523HZ as 27.6 cm, which makes more intuitive sense.

Answer 2

You made a mistake in arithmetic.  L = v/(2*f), so L = 288.64/(2*523) = .276m