Find out the coefficient of linear expansion of the material of an open pipeso that the frequency of any tone emitted from itdoes not very with temperature .

Find out the coefficient of linear expansion of the material of an ope

1.	Find out the coefficient of linear expansion of the material of an open pipeso that the frequency of any tone emitted from itdoes not very with temperature .
Answer» Solution :The fundamental FREQUENCIES at ` 0^(@)` C and` t^(@)` C are respectively , `n_(1) = (V_(0))/(2l_(0)) and n_(2) (V_(t))/(2l_(t))` Here,`V_(0)`= velocity of SOUND at ` 0^(@) C l_(0)`= length of the pipeat ` 0^(@) C , V_(t)` = velocity of sound at ` t^(@) C , l_(t)` = length of the pipe at ` t^(@) C ` . According to the question, ` n_(1) = n_(2)` so , ` (V_(0))/(2l_(0)) = (V_(t))/(2l_(t))` or , `V_(0) l_(t) = V_(t) l_(0) or V_(0) l_(0) (1 + alpha t) = V_(0) ( 1 + 0 .00183 t) l_(0)` [`alpha = ` coefficient of LINEAR expansion] or, ` alpha = 0 . 00183^(@) C^(-1)` .