Respuesta :
Answer:
a) f₀ = 3250 Hz , f₁ = 6500 Hz, b) μ = 0.00100 kg/m
Explanation:
a) For standing waves to occur, waves of equal frequency that travel in opposite directions must be added
In the points where it is fixed there are nodes and in bellies or anti nodes in another symmetrical point
Fundamental wave: node at the ends, a belly (antinode in the center
L = 1 / 2 λ
Extreme node, two bellies L = 2/2 λ
For more bellies L = n / 2 λ
Therefore the equation for the wavelength is
λ = 2 L / n n = 1, 2, 3,…
Let's calculate
λ₁ = 2/1 (2.20)
λ₁ = 4.4 m
λ₂ = 2/2 2.20
λ₂ = 2.20 m
Having the wavelength we can use the relationship of wave speed and wavelength and frequency
v = λ f
v = √ T /μ
v = √ 14.30 / 0.001
v = 14300 m / s
f = v / λ
f₀ = 14300 / 4.4
f₀ = 3250 Hz
f₁ = 14300 / 2.2
f₁ = 6500 Hz
b) linear density is defined as mass per unit length
μ = m / l
μ = 0.0022 / 2.20
μ = 0.001 kg/m
