In this picture why are we summing all frequencies ? what is the reason of summi
ID: 2078191 • Letter: I
Question
In this picture why are we summing all frequencies ?
what is the reason of summing all frequencies and why the constant A is a function of omega i.e w?
this is from the book concepts of thermal physics written by Stephen J.Blundell and Katherine M.Blundell
Which blows up as oo us now solve a problem in which a boundary conditio and a solution is desired in the region r 0. We tions which blow up as r oo and pick the first typ eqn 10.14). Hence our general solution for r 20 can T(ar, t) A (w) exp(-iwt) exp (i -1) e we have summed over all possible frequencies. To fi cies are needed, we have to be specific about the bound hich we want to solve. t us imagine that we want to solve the one-dimension propagation of sinusoidal temperature waves into the d he due to the alternation of day and night (foExplanation / Answer
We can explain this answer by considering the variation of temperature at a particular location and time.
The change in temperature happens at different frequency ranges. Consider a day, the day is hot and the night is cold. This variation has the frequency of 1 day. In a similar way, we can consider a year. The summer season is hot and the winter season is cold. This will have the frequency of 1 year. Similarly, there may be several frequency components available for the variation in temperature. Different frequency components will have different coefficients. The variation of temperature in a particular day will be different than the variation of temperature in a year. The components will provide the range of variations in temperature which will surely depend on the frequency.
T also depends on the location given by x. This location may be latitude and longitude of the place. At a particular time, when there is a winter in the northern hemisphere, there is a summer season in the southern hemisphere. The coefficients will not depend on location x.
The same situation has been considered in the book.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.