Answer:
4) True, the distance was reduced by a de factor 2
Explanation:
To analyze the statements, let's first see how the sound is produced
The cricket makes the sound rubbed its legs, the energy needed to produce it is constant, after the sound is produced it expands in all directions and this wave is subject to the law of energy conservation.
By expanding in all directions we can assume that the energy for the time that is the power of the sound is distributed over a sphere with different radii each time. The perceived intensity is defined as the power per unit area
I = P / A
Where P is the power, A are the areas and I are the intensities heard by the person
Let's clear the power and match, for two different radii (distances)
P = I₁ A₁ = I₂ A₂
The area of a sphere is
A = 4π R₂
I₂ = I₁ A₁ / A₂
I₂ = I₁ 4π R₁² / 4π R₂²
I₂ = I₁ R₁² / R₂²
Let's analyze this last equation for the situation presented if the intensity increases 4 times, substitute
I₂ = 4 I₁
4 I₁ = I₁ R₁² / R₂²
R₂ = R₁ / 2
We see that to increase the intensity 4 times the distance was reduced twice
Now we can analyze the expressions given
2) False, the power is constant, the cricket always does the same job
3) False, the speed of the wave is constant in the air
4) True, the distance was reduced by a de factor 2
