Problem 3
A sound source of frequency is at rest in air where sound speed is . An observer moves directly toward it at speed . Find the observed frequency and its percentage increase over the source frequency. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
problems.proof.stepOf
problems.proof.analysis
Wave crests travel toward the observer at , while the observer moves toward them at ; the encounter speed is their sum. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.
problems.proof.pitfall. Do not mix sign conventions or omit a system constraint; check the sign and units before interpreting the result.