Why is transfer of sound waves not isothermal just like how Newton had assumed?

I tried searching it over the internet but the only result I got that it is just an adiabatic and explaining why the process is adiabatic but my doubt is why is transfer of sound waves not an isothermal. To my knowledge sound is the transfer of energy and in isothermal conditions also energy can be transferred in the form of work. So why is transfer of sound waves adiabatic and not isothermal because locally temperature of air is constant.

Thanks in advance!