Question

Calcula la velocidad del sonido en el aire a 40ºC(313ºK) y una atmosfera de presión (masa molecular del aire M=0,0288kg/mol)

Answer 1

Answer: 355.66 m/s

Explanation:

Since sound is a mechanical wave, its speed varies with the medium and its properties, such as its temperature.

So, if we want to calculate the speed of sound $V$ in air at $40 \° C=313 K$ we can use the following equation that relates $V$ with the temperature:

$V=\sqrt{\frac{\gamma R T}{M}}$ (1)

Where:

$\gamma=1.4$ is the Heat capacity ratio for air

$R=8.314 J/mol.K$ is the Universal Gas constant  

$T=313 K$ is the air temperature in Kelvin

$M=0.0288 kg/mol$ is the air molar mass

$V=\sqrt{\frac{(1.4)(8.314 J/mol.K)(313 K)}{0.0288 kg/mol}}$ (2)

Finally:

$V=355.66 m/s$ This is the speed of sound at 313 K