A violin string vibrates at 441 hz when unfingered. at what frequency will it vibrate if it is fingered one-third of the way down? (only two thirds of the string vibrates.)

f = fundamental frequency of violin = 441 Hz

L = original length of the violin string

v = speed of sound

Fundamental frequency is given as

f = v / (2L)

441 = v / (2L) eq-1

when the string is fingered at one-third of the way down.

L' = new length of the string to vibrate = L - (L/3) = 2L/3

f' = new fundamental frequency of the string

new fundamental frequency of the string is given as

f' = v / (2L')

f' = v / (2 (2L/3))

f' = (3/2) (v / (2L))

using eq-1

f' = (3/2) (441)

f = 661.5 Hz