1. A violin string is 32cm longbetween its fixed ends and has a mass of 2.2g. Th

Question

1.      A violin string is 32cm longbetween its fixed ends and has a mass of 2.2g. The openstring (no finger applied) sounds an A note (440 Hz).

a.       A. Calculate the tension inthe string.

b.     B. What tension would be required for this open string to sound a Cnote (528 Hz)?

c.       C. If instead of changingthe tension you decide to sound a C note by stopping the string(pressing it against the violin with your finger), how far from theend of the string should it be applied?

Please Show ALL work and Formulasused to get the answer. Thank You!

Explanation / Answer

   frequency      f   =   (1/2L)* (T/m)    L   =   Lengthofstring,   T   =   Tensioninstring,    m   =   massperunit length of string   =   2.2 g/ 32 cm    m   =   6.875* 10-3     kg/m    a.  T440   =   f2* 4 * L2 *m                   T440   =   4402* 4 * 0.322 * 6.875 *10-3   =   545.18   N    b.   T528   =   5282* 4 * 0.322 * 6.875 *10-3   =   785.06   N    c.   L   =   (1/2f)* (T/m)                =   (1/2* 528) * (545.18 / 6.875 *10-3)     =      0.267   m   =   26.7   cm          Hencethe string must be stopped at      32- 26.7   =   5.3   cm from theend.          

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