(a) Show that if the temperature changes by a small amount ∆T, the fundamental frequency of an organ pipe changes by approximately ∆f, where ∆f / f = ½ ∆T / T.

(b) Suppose an organ pipe that is closed at one end has a fundamental frequency of 200 Hz when the temperature is 20oC. What will its fundamental frequency be when the temperature is 30oC? (Ignore any change in the length of the pipe due to thermal expansion.)