Question

At what temperature velocity of sound is four times the velocity of sound at temperature 127°c ?

Answer 1

Velocity of sound is directly proportional to square root of absolute temperature.

(v2/v1) = √(T2 / T1)

Where v2 is final velocity, v1 is initial velocity, T2 is final absolute temperature, T1 is initial temperature.

Absolute temperature is equal to degree Celsius plus 273.

Given v2 = 2 × v1, temperature in degree Celsius = 10

Temperature in Kelvin = 10 + 273 = 283

Putting values

(2 × v1)/v1 = √(T2/283)

2 = √ (T2 /283)

Squaring both sides

4 = (T2/283)

T2 = 4 × 283

T2 = 1132 kelvin

Temperature in degrees Celsius = 1132 - 273 = 859 degree Celsius.

At 859 degree Celsius or at 1132 Kelvin temperature velocity will be double the velocity at 10 degree Celsius.

Hope this help.