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.

(a) 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, v.

(b) 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)

For closed end air column,

the 1st standing wave frequency, f1 = v/4L

2nd frequency, f2 = 3*v/4L

f3 = 5*v/4L

f4 = 7v/4L

b)

Now, f1 = 146.83 Hz

So, f2 = 3*f1 = 3*146.83 = 440.49 Hz <-------answer

f3 = 5*146.83 = 734.15 Hz <------answer

f4 = 7*146.83 = 1027.81 Hz <------answer

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