the speed of sound is 331 m/s at 0 °C and increases by 0.6 m/s with each °C increase. But what happens at -1,-2,-3,…etc ?

Answer

There isn’t much of a problem with the speed of sound at negative temperatures.

In general, the speed of sound is determined by the square root of the ratio of elastic modulus and density. Via the ideal gas law, that ratio depends on the temperature. If you fill in the formulas you will come up

c = 331.3 * √[ (273.15+ϑ ) / 273.15] (m/s)

where ϑ is the temperature in degrees Celsius (both positive and negative). One can approximate this last formula around 0°C as

C = 331.3 + 0.606ϑ m/s.

Keep in mind that this last formula is an approximation and only gives good results for temperatures that are not too high or too low.