A steel wire in a piano has mass of 43 grams If tension in w

Solution

Relevant equations to solve the problem are:

1) v = Sqr(Tension(T)/mass per unit length(m/l))

2) v=(wave length(lambda)*frequency(f)

length is not given

mass per unit length = (0.0043kg/l m)

Since we are looking for the fundamental vibration, or first harmonic, and the string is attached at both ends, our wve lenght is (2* lm) or 2l m

Using the second equation, we can solve for v:

v=(2l) *f=523.2 l m/s

Then, we can solve for the tension by pluging our known pieces into the first equation.

523.2 l = Sqr(5.12/m/l)

273738.24 l*m = 5.12

1177 l=5.12

l=4.349 *10^-3 m