Problem 3

A sound source of frequency

f_0

is at rest in air where sound speed is

c

. An observer moves directly toward it at speed

u<c

. 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.prevStep problems.proof.nextStep

\boxed{\frac{f_{\rm obs}-f_0}{f_0}\,100\%=\frac{u}{c}\,100\%}

problems.proof.analysis

Apply the model consistently to each part, then check dimensions and physical limits.