Practice question
Question
A longitudinal wave in a medium has a speed of 1600 m/s and a bulk modulus of 2.56 × 10⁹ Pa. What is
the density of the medium?
Explanation
**Nature of wave** determines energy transfer mechanism. Longitudinal nature of sound explains propagation through fluids with density variations carrying energy, unlike transverse waves needing rigidity for restoring force. Speed: v = √((B/rho)) . 1600 = √((2.56 × 10⁹/rho)) ⇒ 1600² = (2.56 × 10⁹/rho) . rho = (2.56 × 10⁹/1600²) = (2.56 × 10⁹/2.56 × 10⁶) = 1000 kg/m³ . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1000 kg/m³, illustrating frequency-length-speed interdependence and quantization by boundaries.
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