The clarinet is a roughly cylindrical instrument of length L that is open to the

Question

The clarinet is a roughly cylindrical instrument of length L that is open to the outside air at the bell, but closed by the mouthpiece, reed and the player?s mouth at the other end Find expressions for the first four frequencies of standing waves in the clarinet. Your expressions should include the length, L and the speed of sound, y. The lowest note played by a standard clarinet is 146.83 Hz. Use this information and the speed of sound in air, 343 m/s, to find numerical values for the next three frequencies.

Explanation / Answer

(a). First four frequencies of standing waves in the clarinet f = v / 4L

                                                                                   f ' = 3 f = 3v / 4L

                                                                                  f " = 5 f = 5v / 4L

                                                                                 f "' = 7 f = 7v / 4L

(b).The lowest note played by a standard clarniet f = 146.83 Hz

Speed of the sound in air v = 343 m/ s

Next three frequencies f ' = 3 f

                                     = 440.49 Hz

                                 f " = 5 f

                                     = 734.15 Hz

                                f "' = 7 f

                                    = 1027.81 Hz

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