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'. Linear mass density: μ = (0.08/4) = 0.02 kg/m . Speed: v = √((T/μ)) = √((200/0.02)) = √(10000) = 100 m/s . Time: t = (length/v) = (4/100) = 0.04 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.04 s, illustrating frequency-length-speed interdependence and quantization by boundaries.