You are outdoors when you hear the constant chirp of a still cricket. You start walking toward the cricket and at some point you are able to detect that the intensity of the chirp of the cricket has increased by a factor of 4.1) What of the following statements is true at your new position with respect to the cricket?2) The power delivered by the sound wave you hear has doubled.3) The speed of the sound wave emitted by the cricket has decreased by a factor of 4.4) The distance between you and the cricket has decreased by a factor of 2.

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