The function of the ossicles in the middle ear is to transmit the vibrations of

Question

The function of the ossicles in the middle ear is to transmit the vibrations of the tympanic membrane caused by sound waves propagated in air to the fluid-filled cochlea. In doing so, the ossicles change the nature of the vibrations. The ear tries to conserve the energy in the wave I, where v is the wave speed, is the density of the medium, is the frequency of the wave and A is the amplitude of the wave. Calculate the magnitude of the change in A that occurs. The density of air and water is and, respectively, and the velocity of sound is 331 m/s in air and 1410 m/s in water. The frequency of the wave remains constant as the wave propagates. (Hint: Begin with to find.) The bones in the middle ear actually give a reduction of only about 22. This figure should differ from the number you found, but remember that our calculations are only approximate and did not take into account stiffness of membranes and other factors. [10]. [10] Leonard H. Greenberg, PHYSICS FOR BIOLOGY AND PRE-MED STUDENTS, (Philadelphia: W.B. Saunders Co., 1975).

Explanation / Answer

It's simple arithmetic.

Since I and V remain the same it simplifies to:

[ vp A^2 ] (air) = [ vp A^2 ] (water)

or

A^2 (water) / A^2 (air) = vp (air) / vp (water)

Now just plug in the numbers for v and p

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