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The standing wave properties of an ear canal are often modelled as a tube with one...

The standing wave properties of an ear canal are often modelled as a tube with one end open and one end closed. This is shown in the following diagram for a tube of length L = 2.1 cm. The fundamental mode for the sound-pressure standing wave is indicated.The standing wave properties of an ear canal are often modelled as a tube with one end open and one end closed. This is shown in the following diagram for a tube of length L = 2.1 cm. The fundamental mode for the sound-pressure standing wave is indicated.

a) What is the fundamental frequency?

b) Redraw the tube 3 times. Sketch in the standing wave patterns for the 2nd, 3rd and 5th harmonics.

c) What is the wavelength of the 5th harmonic?

d) What is the fundamental frequency if the ear was filled with water?

e) Consider a second tube that is open-open with length L2.

(i) Draw the standing wave pattern for the 3rd harmonic.

(ii) What is L2 so that the 3rd harmonic frequency equals the second harmonic frequency of the ear canal? (assume air-filled for both)

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