Sound, a form of energy can be modeled by using two distinctly different approaches.
a) Describe the propagation of sound energy through air by discussing the motion of individual particles. Include possible mathematical equations that might apply.
Ans: Sound energy propagation via air molecules would be air colliding into each other transferring energy from one molecule to the other and back and forth.
b) describe the propagation of sound energy through air by discussing waves include possible equations that might apply.
Ans: Sound energy propagates in longitudinal wave, which will consist of compression and expansion of air molecules alone the direction of the motion; i.e experiencing medium oscillations along the x-axis.
Are those explanations correct? What mathematical equations do i need to apply?
Yes, your explanations are correct. In order to describe the propagation of sound energy through air using the motion of individual particles (option a), you can use the equations related to particle displacement, velocity, and acceleration.
One possible equation that you can use is the equation of motion for simple harmonic motion. This equation relates the displacement (x), velocity (v), and acceleration (a) of a particle undergoing simple harmonic motion:
a = -ω^2x
where ω is the angular frequency. For a sound wave in air, the angular frequency can be related to the frequency (f) of the sound wave using the equation:
ω = 2πf
Note that the negative sign in the equation signifies that the acceleration and displacement are in opposite directions.
To describe the propagation of sound energy through air using waves (option b), you can use the wave equation, which relates the speed of sound (v), wavelength (λ), and frequency (f) of the sound wave:
v = λf
In this equation, the speed of sound is a constant value that depends on the medium through which the sound is propagating.
These equations can be used to mathematically represent the propagation of sound energy through air, depending on which approach you choose to describe it.