Practice question

**Energy transport** in waves scales with amplitude squared A² and frequency squared ω². Wave speed determines propagation rate, and understanding T and μ allows quantitative prediction of v and associated frequencies. μ = (0.064/3.2) = 0.02 kg/m . v₁ = (v/2L) ⇒ 25 = (v/2 × 3.2) ⇒ v = 25 × 6.4 = 160 m/s . v = √((T/μ)) ⇒ 160 = √((T/0.02)) ⇒ 160² = (T/0.02) . T = 25600 × 0.02 = 512 N . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 512 N, illustrating frequency-length-speed interdependence and quantization by boundaries.