If the intensity level of one trombone is 70 dB, calculate a reasonable estimate for the intensity level of 76 trombones all pla
1 answer:
Answer:
β₂ = 88.8 dβ
Explanation:
The intensity of the sound is
β = 10 log (I / I₀)
The sensitivity threshold (I₀) for humans is 1 10⁻¹² W / m²
I = I₀
I = 10⁻¹² 10^{70/10}
I = 1 10⁻⁵ W / m²
The total intensity for the 76 trombones is
I_total = n I
I_total = 76 1 10⁻⁵
I_total = 76 10⁻⁵ W / m²
Let's find the sound level
β₂ = 10 log (76 10⁻⁵ / 10⁻¹²)
β₂ = 88.8 dβ
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Answer:
A) = 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = + m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase