The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} \mathrm{C}$ to $\alpha^{\circ} \mathrm{C}$. The value of $\alpha$ is ______.

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Waves & Sound

The velocity of sound in air is doubled when the temperature is raised from

0^{\circ} C

α^{\circ} C

. The value of

α

is ______.

Answer: 819

Solution

The speed of sound in a gas varies as

v \propto T

with

T

in kelvin. Doubling the speed requires

\frac{v _{2}}{v _{1}} = 2 = \frac{T _{2}}{T _{1}}

, so

T_{2} = 4 T_{1}

. With

T_{1} = 273 K

(at

0^{\circ} C

T_{2} = 4 \times 273 = 1092 K

. Converting to Celsius,

α = 1092 - 273 = 81 9^{\circ} C

JEE Main · 2026 · 23 Jan 2026 · Shift 2 · Integer answer

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