Respuesta :
Answer:
Δd = 23 cm
Explanation:
When the eta string on the guitar has nodes at its ends, so the waves produced give rise to a standing wave, which can be described by the following expressions
Fundamental L = ½ λ
1st harmonic L = 2 ( λ / 2)
2nd harmonic L = 3 ( λ / 2)
Harmonic n L = n λ / 2
Where n is an integer
The speed of the rope is given by the ratio
v = λ f
This speed is constant since it depends on the tension and the linear density of the rope
Let's calculate the speed with the initial data
v = 0.69 196
v = 135.24 m / s
Let's look for the wavelength for the two frequencies
λ₁ = v / f₁
λ₁ = 135.24 / 233.08
λ₁ = 0.58022 m
λ₂ = v / f₂
λ₂ = 135.24 / 246.94
λ₂ = 0.54766 m
Let's replace in the resonance equation
Lₙ = n λ/2
For the third fret
m = 3
L₃ = 3 0.58022 / 2
L₃ = 0.87033 m
For the fourth fret
m = 4
L₄ = 4 0.54766 / 2
L₄ = 1.09532 m
The distance between the two frets is
Δd = L₄ –L₃
Δd = 1.09532 - 0.87033
Δd = 0.22499 m
Δd = 22.5 cm = 23 cm
The distance that should be far apart the third and fourth frets should be Δd = 3.3 cm.
Calculation of the distance that should be far apart:
Since
The G string should be long i.e. 69 cm.
The frequency is 196 Hz
The third fret from the neck gives B is (233.08 Hz)
And, the fourth fret gives B (246.94 Hz).
So here
L3
= Length * frequency / third fret
= 69*196/233.08
= 58.02 cm
L4
= Length * frequency / fourth fret
= 69*196/246.94
= 54.766 cm
So here the difference should be
= L3 - L4
= 58.02 cm - 54.766 cm
= 3.3 cm
Hence, distance that should be far apart the third and fourth frets should be Δd = 3.3 cm.
Learn more about frequency here: https://brainly.com/question/14498018?referrer=searchResults
