A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10 3 kg/m 3. What is the tension in the wire?

T = 3.590 10³ N

Explanation:

We will solve this exercise in two parts: the first one found the wavelength and the second one the wire tension

For a wire held at the ends we have nodes at these points, so the wavelength is

    L =  λ / 2                             fundametal or 1st harmonic

    L = 2 λ/ 2                            2nd harmonica

     L = 3 λ/ 2                           3rd harmonica

     L = n λ/ 2 n = 1, 2, 3 ...       n harmonica

In this case we have the third harmonic

      L = 3 λ/ 2

      λ = 2/3 L

      λ = 2/3 1.20

      λ = 0.800 m

Let's use the relationship between wave speed

      v = λ f

      v = √T /μ

We substitute

      λ f = √T / μ

     T = λ² f² μ

calculate

     T = 0.8² 512² 21.4 10⁻³

      T = 3.590 10³ N

measuring things 1 litre of water