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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