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,

Question

Philoid · Accepted 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)