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Question

A steel rod of density 7800 kg/m³ has a Young’s modulus of 2 × 10¹¹ Pa. What is the speed of a
longitudinal wave in the rod?

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Explanation

**Sound wave reflection** at rigid wall behaves like string fixed end, displacement inverted. Equation of reflected wave includes sign change and direction reversal, amplitude unchanged but sign may flip, explaining standing wave formation with incident wave. Speed: v = √((Y/rho)) = √((2 × 10¹¹/7800)) ≈ √(2.56 × 10⁷) ≈ 5060 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 5060 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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