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Question

A longitudinal wave in a medium has a speed of 1400 m/s and a density of 800 kg/m³. What is the bulk
modulus of the medium?

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Explanation

**Mechanical waves** require medium and can be transverse or longitudinal. Sound in air is longitudinal since fluids support only compressional motion, while string waves are transverse. Progressive waves transfer energy without net mass transport, distinguishing from standing waves. Speed: v = √((B/rho)) . 1400 = √((B/800)) ⇒ 1400² = (B/800) . B = 1400² × 800 = 1.568 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 1.57 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

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