A steel piano string is 47.4 inches long. The diameter of the string 0.0421 inch

Question

A steel piano string is 47.4 inches long. The diameter of the string
0.0421 inches. When struck, this string produces the musical note B which has the pitch
of 123 Hz. (a) Find the tension of this string. Give the answer in pounds. The density of
steel is 7.86 g/cm3. (b) There are 228 strings in a piano. (Some notes use more than one
string.) If we assume that the tension in every string is the same, find the total force (in tons, 1 ton = 2000 lb) exerted on the frame of the piano. (Add together the tensions of all of the strings.) Piano frames are made of steel so that they can withstand this kind of force.

Explanation / Answer

got my mistake..here it goes frequency f=sqrt(T*L/m)/2*L ==>T=4*f^2*m*l where L=length of string=0.0421 inches=0.1069 cm m=mass of string=density*volume=7.86g/cc *111.252*pi*0.107^2/4=2.5 g=7.86*10^-3 kg f=123Hz a)T=543.9N=543.9 kgm=122.27pounds............ANS (1kg=0.2248 pounds) b)Total force=T*228=27822.27pounds=13.94 tons............ANS hopefully this time its correct :)

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