Answer:
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
