Answer:
[tex]T \approx -20.328^{\circ}C[/tex]
Explanation:
The speed of sound through air as a function of temperature can be estimated by the following first-order polynomic approximation:
[tex]v \approx 331.4\,\frac{m}{s} + \left(0.61\,\frac{m}{s\cdot ^{\circ}C} \right)\cdot T[/tex]
Where:
[tex]v[/tex] - Speed of sound, in meters per second.
[tex]T[/tex] - Temperature, in [tex]^{\circ}C[/tex].
The temperature of air when speed of sound through air is [tex]319\,\frac{m}{s}[/tex] is:
[tex]319\,\frac{m}{s} \approx 331.4\,\frac{m}{s} + \left(0.61\,\frac{m}{s\cdot ^{\circ}C}\right)\cdot T[/tex]
[tex]T \approx -20.328^{\circ}C[/tex]
If speed of sound through air is measure to be 319m/s, the temperature will be -18.15°C or 255 K.
The sound's speed is directly proportional to the square root of temperature.
V = √ RT/M
Thus,
[tex]\bold {\dfrac {V1}{V2} = \sqrt { \dfrac {T1}{T2}}}[/tex]
Where,
V1 - Speed of sound in air = 346 m/s.
V2 - Currunt speed = 319m/s
T1 - Room temperature = 25°C = 298 K = 300 K
T2 - Currunt temperature,
346/319 = √300/T2
1.085 = √300/T2
300/T2 = 1.176
T2 = 300/1.176
T2 = 255 K
Therefore, If speed of sound through air is measure to be 319m/s, the temperature will be -18.15°C or 255 K.
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