You can’t hear temperatures because if the temperatures of air were high enough to make enough noise for you to hear, you would be incinerated.
http://physics.stackexchange.com/questions/110540/how-loud-is-the-thermal-motion-of-air-molecules goes over this. There is a lot of error in that thread, but the parts that are right show up a few times and calculate the white noise sound level of room temperature air at about −20 dB SPL. SPL of 0 dB is the approximate threshold of human hearing. dB is a logarithmic scale such that every 10 dB increase is a 10X higher power. So −20 dB SPL is about 1/100 the average sound power level that would just barely be audible by a human. This is calculated at something close to room temperature, about 23 C which is about 300 K.
How hot would air have to get to have its thermal fluctuations audible as sound to humans? Any thermal power (at sufficiently low frequencies which situation applies here) is proportional to the temperature. So to increase the thermal sound level from −20 dB to 0 dB, the sound power needs to be increased by a factor of 100. So this would happen at an absolute air temperature of 30000 K, or about 29700 C. For us Americans, that is 53500 F. Super crazy hot, hotter than the sun.
So wait a minute, am I saying that a white noise generator generating 0 dB (barely audible) white noise is heating the air to super-solar temperatures? That doesn’t pass the smell test: if it was true my ears would be burning off when exposed to any white noise loud enough for them to hear. But the answer is, we are only generating white noise over a very small frequency range in order to hear it. Even a high fidelity white noise generator will have a bandwidth covering about 50 Hz to 20,000 Hz. But the “natural” bandwidth of thermal fluctuations is found from quantum mechanical considerations: BW = T * kb/h or bandwidth is Temperature(in Kelvin) times Boltzmann’s constant divided by Planck’s constant. That ratio kb/h turns out to be about 20 GHz per degree K. So thermal noise loud enough to hear would have a bandwidth of 600,000 GHz or 6e14 Hz. TO an approximation, thermal power is proportional to bandwidth, so a 20 kHz white noise generator putting out 0 dB SPL is putting out only 20000⁄600000000000 = 1⁄30000000000 the power level associated with a 30000 K source. So in terms of TOTAL energy, a band-limited white noise source is delivering way less than 1 K of extra temperature to your ears, even though in terms of energy density (power per bandwidth), it sounds hotter than the sun.
Much of the thread below covers some of this, but perhaps I add a little detail with what I write. As to blackbody radiation, yes that is appropriate to use here and its upper frequency limit has nothing to do with electromagnetics, or not fundamentally. It is a quantum mechanical limit. At a high enough frequency, the quantum of energy becomes comparable to the thermal energy, and so at higher frequencies than that those frequencies can’t be effectively generated by thermal sources. This is true for both photons (electromagnetic energy quantized) and phonons (sound or vibration energy quantized).
Hope this is clear enough to add more light than heat to the discussion. Or in this case, more sound than heat :)
You can’t hear temperatures because if the temperatures of air were high enough to make enough noise for you to hear, you would be incinerated.
http://physics.stackexchange.com/questions/110540/how-loud-is-the-thermal-motion-of-air-molecules goes over this. There is a lot of error in that thread, but the parts that are right show up a few times and calculate the white noise sound level of room temperature air at about −20 dB SPL. SPL of 0 dB is the approximate threshold of human hearing. dB is a logarithmic scale such that every 10 dB increase is a 10X higher power. So −20 dB SPL is about 1/100 the average sound power level that would just barely be audible by a human. This is calculated at something close to room temperature, about 23 C which is about 300 K.
How hot would air have to get to have its thermal fluctuations audible as sound to humans? Any thermal power (at sufficiently low frequencies which situation applies here) is proportional to the temperature. So to increase the thermal sound level from −20 dB to 0 dB, the sound power needs to be increased by a factor of 100. So this would happen at an absolute air temperature of 30000 K, or about 29700 C. For us Americans, that is 53500 F. Super crazy hot, hotter than the sun.
So wait a minute, am I saying that a white noise generator generating 0 dB (barely audible) white noise is heating the air to super-solar temperatures? That doesn’t pass the smell test: if it was true my ears would be burning off when exposed to any white noise loud enough for them to hear. But the answer is, we are only generating white noise over a very small frequency range in order to hear it. Even a high fidelity white noise generator will have a bandwidth covering about 50 Hz to 20,000 Hz. But the “natural” bandwidth of thermal fluctuations is found from quantum mechanical considerations: BW = T * kb/h or bandwidth is Temperature(in Kelvin) times Boltzmann’s constant divided by Planck’s constant. That ratio kb/h turns out to be about 20 GHz per degree K. So thermal noise loud enough to hear would have a bandwidth of 600,000 GHz or 6e14 Hz. TO an approximation, thermal power is proportional to bandwidth, so a 20 kHz white noise generator putting out 0 dB SPL is putting out only 20000⁄600000000000 = 1⁄30000000000 the power level associated with a 30000 K source. So in terms of TOTAL energy, a band-limited white noise source is delivering way less than 1 K of extra temperature to your ears, even though in terms of energy density (power per bandwidth), it sounds hotter than the sun.
Much of the thread below covers some of this, but perhaps I add a little detail with what I write. As to blackbody radiation, yes that is appropriate to use here and its upper frequency limit has nothing to do with electromagnetics, or not fundamentally. It is a quantum mechanical limit. At a high enough frequency, the quantum of energy becomes comparable to the thermal energy, and so at higher frequencies than that those frequencies can’t be effectively generated by thermal sources. This is true for both photons (electromagnetic energy quantized) and phonons (sound or vibration energy quantized).
Hope this is clear enough to add more light than heat to the discussion. Or in this case, more sound than heat :)