a pipe organ is tuned at a particular temperature.the organ is in tune when the

Question

a pipe organ is tuned at a particular temperature.the organ is in tune when the room temperature is 20 C .The diapason is the name of an organ stop that produces the typical organ sound. the pipe is open at both ends.
a) If the length of the pipe is 2.40 m , what is the fundamental frequency of the pipe at this temperature .
b)On a hot summer day , the room temperature rises to 25 C . what is the new fundamental frequency ?
c)What is the ratio of the fundamental frequency at 25 C to that at 20 C ?

Explanation / Answer

Length pipe L = 2.4 m Speed of sound at 20 o C is v = 343.2 m / s So, fundamental frequency f = v / 2L                                             = 71.5 Hz (b). Speed of sound at 25 o C is v ' = 346.13 m / s So, fundamental frequency f ' = v ' / 2L                                             = 72.11 Hz (c).The ratio of the fundamental frequency at 25 o C to that at 20 o C = f ' / f                                                                                                          = 1.0085 So, fundamental frequency f ' = v ' / 2L                                             = 72.11 Hz (c).The ratio of the fundamental frequency at 25 o C to that at 20 o C = f ' / f                                                                                                          = 1.0085

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