Practice question

**Doppler effect** describes apparent frequency shift due to relative motion between source and observer, f' = f·v/(v ∓ v_s) for source motion, f' = f·(v ± v_o)/v for observer motion, upper signs for approach increasing observed frequency. Motion towards observer compresses wavelength raising f'. The speed v = √((T/μ)) depends on tension and mass density, properties of the medium, not frequency, which is source-dependent. Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields Medium properties, illustrating frequency-length-speed interdependence and quantization by boundaries.