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What is the temperature if the speed of sound through air is measure to be 319m/s? PLEASE SHOW YOUR WORK

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Answer: Temperature = 255K

Explanation: Given that the speed of sound through air is measure to be 319m/s

Speed of sound is proportional to the square root of temperature. That is

V = √ RT/M

Therefore,

V1/V2 = √ T1/T2

The speed of sound in room temperature air is 346 meters per second.

room temperature is taken to be about 20 to 25 degrees Celsius with an average of 23 °C or 300 K is often used.

346/319 = √ 300/T2

1.085 = √ 300/T2

300/T2 = 1.176

T2 = 300/1.176

T2 = 255K

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