I have recently been intrigued by the following question: What is the difference between the pitch of the noise of dripping water between hot and cold water? For example, would cold water create a higher pitched noise while dripping into a pot of water? Or vice versa?
Taking into account some facts:
The speed of sound C is 343.2 m/s
In air the speed increases 0.6 m/s per degree Celsius
Also, the just-noticeable difference (jnd) in pitch depends on the tone's frequency. Below 500 Hz, the jnd is about 1 Hz for complex tones; above 1000 Hz, the jnd for sine waves is about 0.6% (6 Hz).
As the speed of the sound varies with temperaute, also does the product of the wave length mutiplied by the frecuency.
For the most part the dimensions changes due to temperature changes in the vibrating object that produces the sound are imperseptible; In which case the wave lengt would remains constant.
So the speed changes due to temperature are in the same proportion of frecuency changes.
Bellow 500 Hz, would be needed a 0.2% change (1Hz/500Hz) in frecuency, to be able to perceive any change. As the speed change needs to be the same, the speed change is also 0.2%
C = 343.2 m/s (speed of the sound)
So, the speed change needed is 0.6864 m/s, wich is (0.2%)
The temperature change needed would the change in speed needed divided by 0.6 m/sºC, wich is 1.144 ºC
Above 1000 Hz,
Would be needed a 0.6% change in frequency
Then the speed change needed is 2.0592 m/s
The temperature change needed woudl be 3.432 ºC
Unless the ambient temperature changes 1.144 ºC, it won't be likely to hear any pitch change, as the change in dimension of the vibrating body are negligible
Please, feel free to review and correct if needed