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How does temperature affect the speed of sound in a solid? Given v0 = 1000 ms⁻¹ at 0°C, find vT using vT = v0 (1 + αT).

Physics

ScanSolve AI Answer

Step-by-step solution

3 steps
  1. Identify the given values.

    The speed of sound in the solid at 0∘C0^\circ\text{C} is v0=1000 ms−1v_0 = 1000 \text{ ms}^{-1}.
    The temperature change is from 0∘C0^\circ\text{C} to 25∘C25^\circ\text{C}.

  2. Use the formula for the speed of sound as a function of temperature.

    For many materials, the speed of sound changes approximately linearly with temperature. The general formula is:

    vT=v0(1+αT)v_T = v_0 (1 + \alpha T)

    where vTv_T is the speed at temperature TT, v0v_0 is the speed at 0∘C0^\circ\text{C}, and α\alpha is the temperature coefficient of the speed of sound.

  3. Determine the temperature coefficient α\alpha that matches one of the options.

    Let

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