The portion of a violin string that vibrates (from the “bridge” to the “nut” at

Question

The portion of a violin string that vibrates (from the “bridge” to the “nut” at the end of the finger board) is 60.0 cm long and has mass 2.00 g. When played, the string produces an A note of 440 Hz as its fundamental frequency. a) At what distance from the bridge should the violinist put her finger to play a B note of 494 Hz (as the string’s fundamental frequency)? b) Is it possible to play a D note of 294 Hz (as the string’s fundamental frequency) on this string without retuning (changing the string tension)? Explain why or why not.

Explanation / Answer

a) Let L is the actual length of the string.

Let L' is the effective length when the player plays B note.

fA/fB = (v/2*L)/(v/(2*L')

fA/fB = L'/L

==> L' = L*fA/fB

= 60*440/494

= 53.44 cm

so, at L - L = 60 - 53.44

= 6.56 cm from the bridge the violinist put her finger

b) Its not possible. The lowest frequency produced(funda metnal) by the string is 440 Hz.

so, we can not produce less freqency sound than 440 hz with out tuning.

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