Sound is air particles vibrating (thus hitting each other to make longitudinal waves) and heat is the vibration of air molecules. Because we can only assume that heat made from fire is a higher intensity of vibration than sound (because we don't burn ourselves when we speak) why doesn't it make an extremely loud sound?
Thermodynamics – Why Does Fire Make Very Little Sound? Acoustics and Waves
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Best Answer
The combustion reactions don't inherently make any sounds. But they release plenty of energy causing the nearby molecules to acquire higher random kinetic energy, which is theoretically detectable as Brownian noise. But it's not as easy as detecting a human's speaking because the noise is indistinct and the power at the eardrum is lower: a lot of the particles' velocities aren't towards the eardrum so a limited amount of energy is transferred. Unlike longitudinal sound waves, where groups of particles oscillate periodically with large amplitudes, the movement here is rather disorganized and isn't audible for all reasonable temperatures, so you're more likely to hear the sound of wood popping due to the expansion of fibres and escape of moisture and air, or sounds of wind blowing as air expands and rises rapidly.
I decided to take a shot at finding the temperature needed for the Brownian noise to be about as loud as a conversation. For $60\ \rm dB (SPL)$, with the usual reference of $2\times 10^{-5}\ \rm Pa$ and considering the ear's highest sensitivity region, we're looking for an eventual rms pressure of $2\times 10^{-2}\ \rm Pa$. Using the equation from On Minimum Audible Sound Fields by Sivian and White$$\bar{P} =\left [ \frac{8 \pi \rho k_B T} {3c} ({f_2}^3-{f_1}^3)\right ]^{1/2}$$where $\bar{P}$ is the rms (root mean square) pressure, $\rho$ is the density of air, $k_B$ is the Boltzmann constant, $T$ is the temperature, $c$ is the speed of sound in air, and $f_1$ and $f_2$ are the frequency range. Let's consider the frequency range of $0\ \rm Hz$ to $2\times 10^4\ \rm Hz$, because according to the Brownian frequency distribution, higher frequencies are negligible. Throwing in common values for all the constants, we see that for $\bar{P}=2\times 10^{-2}\ \rm Pa$, we need an unbelievable $10^8\ \rm K$, to 1 significant figure, which is hotter than the Sun's core.
It's important to not think that this implies that we're never going to hear Brownian noise. If you take some software like Audacity (or probably any sound editing tool), you can render Brownian noise and listen to it at $60\ \rm dB$. But there we have a deliberate superimposition of several frequencies' waveforms (with amplitudes according to the distribution) being played. But we won't hear the noise caused by the random kinetic energy of air molecules at a loudness comparable to normal conversations.
"Because we can only assume that heat made from fire is a higher intensity of vibration than sound" isn't really true: because of the direction of particles' oscillations/movement, longitudinal sound waves end up transferring far more energy to the ear drum.
Eventually, we're not going to detect the noise; the flows due to convection and expansion of hot air are more likely to be audible.
And some cool related stuff: Difference between sound and heat at particle level