Question

Using the Laplace formula, calculate the velocity of sound for air. Given g = 1.4,
r = 1.29 kg m−3 and p = 1.01 × 105 Nm−2.

Answer 1

Answer on Question 74849, Physics, Molecular Physics, Thermodynamics

Question:

Using the Laplace formula, calculate the velocity of sound for air. Given $\gamma = 1.4$, $\rho = 1.29\, kgm^{-3}$ and $P = 1.01 \cdot 10^{5}\, Nm^{-2}$.

Solution:

The velocity of sound for air can be found from the Laplace formula:

$$v = \sqrt{\frac{\gamma P}{\rho}},$$

here, $\gamma$ is the adiabatic index, $\rho$ is the density of air and $P$ is the pressure.

Then, we get:

$$v = \sqrt{\frac{\gamma P}{\rho}} = \sqrt{\frac{1.4 \cdot 1.01 \cdot 10^{5} \, \frac{N}{m^{2}}}{1.29 \, \frac{kg}{m^{3}}}} = 331 \, \frac{m}{s}.$$

Answer:

$$v = 331 \, \frac{m}{s}.$$

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