Respuesta :
The characteristics of the speed of the waves in strings and the resonance allows to find the change in the fundamental frequency when changing the tension is:
- The change in fundamental frequency is: f = 1.08 f₀
The speed of the chord wave is given by the relationship between the tension and the density of the medium.
[tex]v= \sqrt{\frac{T}{\mu } }[/tex]
Where v is the velocity of the wave, T the tension of the string and μ the density
In a rope held at the ends, a process of standing waves occurs, two at the point where it is attached we have a node and a anti-node in the center.
2L = n λ
Where L is the length of the chord and call the wavelength
Wave speeds are related to wavelength and frequency.
v = λ f
We substitute.
[tex]\sqrt{\frac{T}{\mu } } = \frac{2L}{n} \ \ f[/tex]
For the fundamental frequency n = 1
f₀ = [tex]f_o = \sqrt{\frac{T}{\mu } } \ \ \frac{1}{2L}[/tex]
They indicate that the tension increases 1.70%
T = T₀ + 0.17 T₀
T = 1.17 T₀
We substitute.
[tex]f = \sqrt{1.17 } \ \sqrt{\frac{T_o}{\mu } } \ \ \frac{1}{2L}[/tex]
f = ra1.17 f₀
f = 1.08 f₀
In conclusion, using the characteristics of the velocity of the waves in strings and the resonance we can find the change in the fundamental frequency when changing the tension is:
- The change in fundamental frequency is: f = 1.08 f₀
Learn more about string resonance here: brainly.com/question/16010929
