Problem 3

A sound source of frequency

f

moves directly toward a stationary listener at speed

u<c

in air where sound speed is

c

. Find the observed frequency. Use an idealized laboratory-frame model: stated parameters remain constant during the process unless the motion itself makes a quantity vary. State a clear sign convention and use the defined symbols consistently. (a) Write the governing laws or constraints. (b) Derive the requested quantities symbolically and state their physical direction or meaning. (c) Check dimensions and examine a simple physical limit to validate the result. Finally, verify that every equation is dimensionally consistent and that the results satisfy the initial conditions. Since no numerical data are specified, the exact answers are expressions in the defined symbols.

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

u\to0:f_{\rm obs}\to f;\quad u\to c^-:f_{\rm obs}\to\infty

problems.proof.analysis

A simple limit or independent law provides a cross-check. If the result contradicts the expected physical trend, revisit the signs, approximations, or boundary conditions.