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Question

A steel rod of length 1.2 m has a fundamental frequency of longitudinal vibrations of 2.5 kHz. What is
the speed of sound 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. For rod clamped at middle, fundamental: v₁ = (v/2L) . 2500 = (v/2 × 1.2) ⇒ v = 2500 × 2.4 = 6000 m/s . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 6000 m/s, illustrating frequency-length-speed interdependence and quantization by boundaries.

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