One face of a thick uniform layer is subject to sinu- soidal temperature variations of angular frequency w. show that damped sinusoidal temperature oscil- lations propagate into the layer and give an expres- sion for the decay length of the oscillation ampli- tude. a cellar is built underground and is covered by a ceiling, which is 3 m thick and made of lime- stone. the outside temperature is subject to daily fluctuations of amplitude 10°c and annual fluctua- tions of 20°c. estimate the magnitude of the daily and annual temperature variations within the cel- lar. assuming that january is the coldest month of the year, when will the cellar's temperature be at its lowest?