A steel piano wire is 42in long and has a diameter of 00254

A steel piano wire is 42in long and has a diameter of 0.0254 in. What tension (in lbs) should be applied to the wire to make it produce a fundamental frequency of 264 Hz?

Solution

The equation for the fundamental frequency of a wire as a function of tension, length, diameter and density of the wire material is:

F = (1/Ld)*(T/) -eqn(1)

where, F is the frequency in hertz (Hz) ,L is the length of the wire ,d is the diameter of the wire ,T is the tension on the wire , is the Greek letter pi = 3.14 , is the density of the wire in lb/in³ usually,piano wires are made of carbon steel (density =0.2839605 lb/in³ )

substitute F= 264 ,L =42 ,d= 0.0254 , = 0.2839605lb/in³

264*42*0.0254 =(T/3.14*0.2839605)

now Tension (T)=70768.84lbs