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Question

A longitudinal wave in a medium has a speed of 1550 m/s and a density of 1200 kg/m³. What is the bulk
modulus of the medium?

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Explanation

**Sinusoidal wave form** represents harmonic wave where each particle executes SHM. Coefficients of x and t give spatial and temporal periodicities, allowing wavelength and period extraction, basis for wave analysis in NCERT. Speed: v = √((B/rho)) . 1550 = √((B/1200)) ⇒ 1550² = (B/1200) . B = 1550² × 1200 = 2.88 × 10⁹ Pa . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 2.88 × 10⁹ Pa, illustrating frequency-length-speed interdependence and quantization by boundaries.

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