With a particular fingering, a flute plays a note with frequency879 Hz at 20.0°

Question

With a particular fingering, a flute plays a note with frequency879 Hz at 20.0° C. The flute isopen at both ends. (a) Find the air column length.
1 m

(b) Find the frequency it produces at the beginning of the halftimeperformance at a late-season American football game, when theambient temperature is -3.73°C and theplayer has not had a chance to warm up the flute.
2 Hz (a) Find the air column length.
1 m

(b) Find the frequency it produces at the beginning of the halftimeperformance at a late-season American football game, when theambient temperature is -3.73°C and theplayer has not had a chance to warm up the flute.
2 Hz

Explanation / Answer

Frequency f = 879 Hz temperature T = 20 oC = 20 + 273 = 293 K velocity of sound v = 343 m / s we know frequency f = v / 2L from this length of air column L = v / 2f                                                = 0.195 m (b). speed at temperature t ( = -3.73 oC ) is v ' =331 [ 1 + ( t / 546 ) ]                                                                         =331 [ 1 + ( -3.73 / 546 ) ]                                                                        = 328.73 m / s frequency f ' = v ' / 2L                     =842.92 Hz

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