13) With a particular fingering, a flute plays a note withfrequency 583 Hz at 20

Question

13) With a particular fingering, a flute plays a note withfrequency 583 Hz at 20.0° C. The fluteis open at both ends. (a) Find the air column length.
m
(b) Find the frequency it produces at thebeginning of the halftime performance at a late-season Americanfootball game, when the ambient temerature is -5.66°C and the player has not had a chance towarm up the flute.
Hz (a) Find the air column length.
m
(b) Find the frequency it produces at thebeginning of the halftime performance at a late-season Americanfootball game, when the ambient temerature is -5.66°C and the player has not had a chance towarm up the flute.
Hz

Explanation / Answer

a ) frequency f   = 583Hz   , Temperature Tc =200 C                 speed of the sound is v = ( 331 m/s +0.6*TC )                                                         = ( 331 m/s + 0.6 * 20 )                                                         = 343 m/s                          For Open Pipe f = n v / 2 L                                              583 Hz = 1 * 343 m/s / 2 L                                                L = 0.294 m b )   speed of the sound v = ( 331m/s + 0.6 * ( -5.66 )                                          = 327.6 m/s                      f    = n v / 2 L                           = 1 * 327.6 m/s / 2 ( 0.294 m )                           = 557 Hz

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