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, cramster-equation-2010731130406341613664 is the density of the medium, cramster-equation-2010731131286341613668 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 1.3x10–3g/cm3 and 1.0g/cm3, 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 .)

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Answer: The magnitude of the change in A is 8.55 dB. Explanation: We can use the conservation of energy equation to calculate the magnitude of the change in amplitude: I = I0*(v/v0)^2 * (rho/rho0) Where I0 is the initial intensity, v0 is the initial speed of sound, and rho0 is the initial density of the medium. We can rearrange this equation to solve for the change in amplitude: A2/A1 = (v0/v)^2 * (rho/rho0) For this problem, we have an initial speed of sound in air (331 m/s) and an initial density of 1.3 x 10-3 g/cm3, and a final speed of sound in water (1410 m/s) and a final density of 1.0 kg/m3. Plugging these values into the equation above gives us: A2/A1 = (331/1410)^2 * (1.0/1.3 x 10^-3) = 81.82 We can then take the logarithm of this value to get the magnitude of the change in amplitude in decibels (dB): log (81.82) = 8.55 dB Therefore, the magnitude of the change in A is 8.55 dB.
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