The lowest note on a piano is 27.5 Hz. if strings with v=84.7 m/s are used, how long should the piano string be? unit= m

Explanation:

The lowest note on the grand piano is the fundamental harmonic, meaning that the wavelength is twice the length of the vibrating section of the string, λ = 2L, where L = 1.90 m. The speed of the wave is v = λf, but also depends on the tension of the wire as v =qT µ, where µ = m/` is the linear mass density of the wire (` is the full length of the wire, not the vibrating part). So, solving for the tension gives

2

With numbers we find

which is a pretty big amount of force!

RESULT

2185 N See explanation

total distance/total time

(85 + 82)/(5+3)

167/8

20 just over