Question

2. ๒ class we have discussed the general concept of impedance matching to achieve maximum efficiency of the transfer of energy from one medium or system into another. For example, in an electrical systom where a source of electrical power is transferring energy to a load, you have leaned that maximum power impedances are matched, Le. where the real parts (resistance) are equal, and the reactance cancels. One of the many physiological systems in which impodance matiching is important is that transfer is achieved when the source and load of the auditory system, in which sound energy from the air must be coupled into the fluid medium in the inner car, where the significant density difference between air and water, a serious acoustic impedance mismatch exists, and most of the sound energy would reflect off your inner ear struacture (ie. the oval window) were there not some physiological design to overcome this problem. sensory cells exist. We discussed in class that because ofthe As a demonstration of this general principle, consider the case of the collision of two balls having the same diameter, but different masses (iediffcrent dansities). Ifthe masses are not the same, we observe that the impacting ball will cither reflect (mm) or retain some forward momentum (mom).This can be thought of as being due to an impedance mismatch with the first case being analogous to the mismatch between air and water that exists in your auditory system. If the two masses are the same, the impedance is mtcbed, and the energy from the first ball is completely transferred to the second To examine this effect mathematically, consider a ball of mass ml traveling at velocity vi impacting a ball at rest having mass m, as shown: m, m. Let the velocity of the second ball after impact be vs and the velocity of the first ball after impact be v (a) Starting with the basic oquations for conserving energy and momentum, calculate the post- impact velocities of the two balls assuming m- 0.2ms Momentum is a vector quantity, of course, i.e. is directional, while kinetic energy is not, so be sure to indicate the direction of the velocity results (b) Use your result from part (a) to calculate the relative efficiency in % of the kinetic energy transfer from the first ball to the second ball (c) Repeat the calculation from part (a) for m-1.25 m (d) In actuality, air is approximately 800 times less dense than water. Use this fact to repeat the calculations of parts (a) and (b) where m,-m/800. (e) Based on your results from part (d), comment on how important you think it is to have an

Answer 1