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Question

A longitudinal wave in a medium has a speed of 1600 m/s and a density of 1250 kg/m³. What is the bulk
modulus of the medium?

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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 = √((B/1250)) ⇒ 1600² = (B/1250) . B = 1600² × 1250 = 3.2 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 3.2 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

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