Waves

JEE Main level, numerical answer, medium

127 of 142

Question 127 of 142

The velocity of sound in air is doubled when the temperature is raised from 0∘C0^{\circ} \mathrm{C} to α∘C\alpha^{\circ} \mathrm{C}. The value of α\alpha is ____\_\_\_\_.

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Answer: 819

The velocity of sound in air depends on temperature as v∝Tv \propto \sqrt{T} (absolute temperature).
If the velocity doubles:
v2v1=2=T2T1\frac{v_2}{v_1} = 2 = \sqrt{\frac{T_2}{T_1}}.
Squaring: T2T1=4\frac{T_2}{T_1} = 4.
With T1=0°C=273.15T_1 = 0°C = 273.15 K and T2=273.15+αT_2 = 273.15 + \alpha K:
273.15+α273.15=4\frac{273.15 + \alpha}{273.15} = 4, giving 273.15+α=1092.6273.15 + \alpha = 1092.6 K.
Therefore α=819.45°C≈819°C\alpha = 819.45°C \approx 819°C.

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