Someone argues: "Sound waves spread out spherically from a moving body at the speed…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Waves, acoustics and compressible flow · Waves, acoustics and compressible flow
Signal Speeds in Fluids, Ch Steady compressible flow: energy, stagnation and the Mach number
Problem
Someone argues: "Sound waves spread out spherically from a moving body at the speed of sound c in every direction, including forwards. So even a supersonic aircraft must push a wave of compressed air ahead of itself, warning the air of its arrival before it gets there, exactly as a subsonic aircraft does; the only difference is that this warning is weaker." Consider a body moving steadily at M∞=1.6 through still air.
((a)) Is the claim correct? Justify the answer by comparing the body's speed with the speed at which a disturbance it emits can travel upstream (against the oncoming flow, in the body's own frame).
((b)) Calculate the Mach angle μ for M∞=1.6.
((c)) Describe, in the body's frame, the boundary of the region that has felt no disturbance from the body, and state whether that boundary is ahead of or behind the body.