Practice question

**Frequency shift** proportional to source speed relative to wave speed v. Understanding sign convention for approaching versus receding is key, with approaching increasing frequency and receding decreasing, central to Doppler applications. Linear mass density: μ = (mass/length) = (0.01/2) = 0.005 kg/m . Speed: v = √((T/μ)) = √((100/0.005)) = √(20000) ≈ 141.4 m/s . Time: t = (length/v) = (2/141.4) ≈ 0.014 s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 0.014 s, illustrating frequency-length-speed interdependence and quantization by boundaries.