Final answer:
When a parcel exceeds its specific volume (SVP), the volume and pressure within it change inversely based on the displacement caused by sound waves. An increase in volume leads to decreased pressure, while a decrease in volume leads to increased pressure, as shown in the mathematical expression AV = AΔS and the limitation equation for fractional volume change.
Step-by-step explanation:
When a parcel exceeds the specific volume of a parcel (SVP), various changes occur within the parcel in regards to pressure and volume due to sound waves moving through it. If s2 is greater than s1, the volume of the parcel has increased resulting in a decreased pressure. Conversely, if s2 is less than s1, the volume has decreased and the pressure within the parcel has increased. The quantitative change in the parcel's volume can be expressed as AV = AΔS = A (S₂ - S₁) = A (s (x + Δx, t) - s (x, t)). To determine the fractional change in the volume, this volume change is divided by the original volume, which is mathematically represented as:
dV = lim ΔV / V Δx→0 = A[s (x + Δx, t) - s (x, t)] / (s (x, t) AΔx).
Understanding the Effects on Pressure and Volume
When a sound wave impacts the parcel causing it to exceed its SVP, the pressure and volume adjustments are a direct result of the physical properties of gases and their responses to changes in conditions. Depending on whether the volume increases or decreases, the pressure will adjust in an inverse relationship. This is a fundamental aspect of how sound waves interact with the medium they move through under the principals of physics and specifically the study of acoustics.