Question

Find the ratio of initial and final velocity of sound if absolute temperature is doubled.

Answer 1

Velocity of sound is given as

$v=20.05 \sqrt{T}\ m/s\\ where\ T=absolute\ temperature\ of\ air.$

(Absolute temperature is temperature in Kelvin.)
When temperature is doubled, let say from T to 2T, velocity will be

$v=20.05 \sqrt{T} \\v'=20.05 \sqrt{2T}= \sqrt{2} \times 20.05 \sqrt{T}\\ \\ \frac{v'}{v}= \frac{ \sqrt{2} \times 20.05 \sqrt{T}}{20.05 \sqrt{T}} =\boxed{ \sqrt{2} }$

Answer 2

velocity of sound  v is proportional to  the absolute temperature T of the ideal gas through which it travels.

       v  α  √T
   v2 / v1 = √(T2 / T1) = √2
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More formulas:
    Actually through an ideal gas, velocity of sound (longitudinal wave):
       v = 20.05 √T  m/sec
       v = √ [ γ R T / M]
             γ = ratio of specific heats of the gas
             R = universal gas constant
             M = molar mass of the gas