"Vibrato" in a violin is produced by sliding the finger back and forth along the vibrating string. The G-string on a particular violin measures 30cm between the bridge and its far end and is clamped rigidly at both points. its fundamental frequency is 197Hz
(a) how far from the end should the violinist place a finger so that the G-string plays the note A(440Hz)?
(b)If the violinist executes vibrato by moving the finger 0.50 cm to either side of the position in part(a),what is the resulting range of frequencies?
The Attempt at a Solution
i assume speed of wave would remain the same so v=f1x(2L)=118.2m/s
as the rigid end of the string is node,so the finger should be put at next node which is 0.5λ away,that is 0.269/2=0.134m, but the answer is 0.166m. also i think n should be whole numbers but in this case i couldn't get n to be a whole number.