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 approach (a), where you describe the motion of individual particles, you can use the concept of simple harmonic motion to explain the motion of air molecules. As sound travels through air, the air particles vibrate back and forth in a sinusoidal manner, creating areas of compression and rarefaction. This motion can be described using the equation for simple harmonic motion:
x = A sin(ωt + φ)
where x is the displacement of the particle from its equilibrium position, A is the amplitude of the vibration, ω is the angular frequency, t is the time, and φ is the phase constant.
In approach (b), where you discuss waves, you can use the mathematical equations that describe the properties of waves. For example, the velocity of sound in air can be determined using the wave equation:
v = fλ
where v is the velocity, f is the frequency of the wave, and λ is the wavelength. The frequency of a sound wave can be measured in Hertz (Hz) and the wavelength in meters (m).
Additionally, you can also use the general equation for a wave:
y(x, t) = A sin(kx - ωt + φ)
where y is the displacement of a particle, x is the position, t is the time, A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase constant. This equation represents the propagating wave nature of sound.
Keep in mind that these equations are just examples and there are other mathematical equations and models that can be used to describe sound propagation through air. The specific equation to be used depends on the specific aspects or properties of sound you want to analyze or calculate.