Question

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at what temperature the velocity of sound in air is two times its velocity at 10 degree centigrade

Answer 1

What is the temperature at which the velocity of sound in air is twice its velocity at 10C?

Answer



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.
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Answer 2

The velocity temperature is equal to celsious plus 273.

Temperature in Kelvin = 10 + 273 = 283

Squaring both sides

4 = (T2/283)
T2 = 4×283
T2 = 1132 Kelvin