A violin string is 0.42 m long. It produces the musical note A (440 Hz) when pla

Question

A violin string is 0.42 m long. It produces the musical note A (440 Hz) when played without fingering. This means that when the string has its full length, and is fixed at both ends, it has a frequency of 440 Hz in its fundamental (longest wavelength) mode (a) What is the speed of the wave on the string? To play a C note (523 Hz), you have to hold the string down with your finger, effectively shortening the string, while it is still fixed at both ends (b) How far from the end of the string should you place your finger to play a C (523 Hz)? In other words, what is the length of the string when it vibrates at the new m/s frequency?

Explanation / Answer

(A) for fundamental vibration,

L = lambda / 2

lambda = 2 L = 0.84 m

v = f lambd = 0.84 x 440 = 369.6 m/s

(B) v = f lambda = constant

369.6 = 523 lambda

lambda = 0.707 m

L = lambda / 2= 0.353 m

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