Q. 52

Show that if the room temperature changes by a small amount from T to T + ∆T, the fundamental frequency of an organ pipe changes from v to v + ∆v, where,



Answer :

Let be the frequency of an open pipe at a temperature T. When the fundamental frequency of an organ pipe changes from to , the temperature changes from T to.


We know that:
----------- (i)


According to the question,



Applying this in equation (i), we get:




By expanding the right-hand side of the above equation using the binomial theorem, we get:


(Neglecting the higher terms)



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