Calculating Tension for Steel Wire in Piano

[Machine]

Homework Statement

Question: Standing Waves:

A steel wire in a piano has a length of 0.7000m and a mass of 4.300 x 10^-3 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fc=261.6 Hz on the chromatic musical scale)?

Homework Equations

f1=v/wave1 = v/2L

The Attempt at a Solution

f1=v/2L
v=2Lf1= (.7000m)(261.6Hz)= 183.12 m/s

 

[mukundpa]

Can you differentiate between the two velocities?

(1) Velocity of sound wave in air which is produced by vibrating wire.

(2) Velocity of transverse wave in a stretched string.

 

[chaoseverlasting]

You know the speed required right? And the speed of sound in a string is given by $$v=\sqrt{\frac{T}{\mu}}$$ where $$\mu$$ is the mass per unit length.