studyhero A violin string has a length, from the bridge to the end of the fingerboard, of 50 cm. That section of the string has
a mass of only 2 g. When the violinist plays an open string (the full length) a 440 Hz A-note is heard. Determine the length of the string needed to play a 528 Hz note without adjusting the tension in the string. This is accomplished by pressing on the fingerboard at the appropriate location.
This is a resonance exercise where the ends of the string are fixed, therefore it has a node of them, the fundamental (longest) wavelength created has the form
λ = 2L
wave speed is related to wavelength and frequency
v = λ f
v = 2L f
let's calculate
v = 2 0.50 440
v = 440 m / s
since they indicate that the tension of the string does not change and the linear density of the string is constant, the speed of the wave also remains constant
f =
let's find the length for the new resonance frequency