Concept:Temperature provides gas molecules with higher kinetic energy, allowing them to collide and transfer sound pressure waves more rapidly.
Formula:$$ v_t = v_0 + 0.61t $$
Solution:- Derivations from the ideal gas law and Laplace's formula show that the speed of sound in air is proportional to the square root of absolute temperature.
- For small temperature variations near \( 0^\circ\text{C} \), this relationship simplifies to a linear approximation.
- Experimentally and theoretically, for every \( 1^\circ\text{C} \) increase in temperature, the speed of sound climbs by a constant factor of exactly \( 0.61 \text{ m/s} \).
Why other options are incorrect:The values 0.51, 0.41, and 0.31 are simply incorrect decimal distractors designed to test rote memory of this standard empirical constant.
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