If the form of a sound wave traveling through air is s(x, t)=(6.0 nm)cos(kx+(3000 rad/s)t+ϕ) how much time does any given air molecule along the path take to move between displacements s=+2.0 nm and s=−2.0 nm?

answer: the potential energy decreases from 379 j to 243 j

explanation:

for the law of conservation of energy, the total energy in a system must be conserved. the total energy of the system is given by the sum of kinetic (k) and potential (u) energy:

e = k + u

the total energy is e=675 j, and this does not change.

initially, the kinetic energy is k=296 j, so the potential energy is

at the end, the kinetic energy is k=432 j, so the potential energy is

so, we see that the potential energy has decreased from 379 j to 243 j.