The ability to hear a \"pin drop\" is the sign of sensitive hearing. Suppose a 0

Question

The ability to hear a "pin drop" is the sign of sensitive hearing. Suppose a 0.50 gram pin is dropped from a height of 27 cm, and that the pin emits sound for 1.4 seconds when it lands. Assuming all of the mechanical energy of the pin is converted to sound energy, and that the sound radiates uniformly in all directions, find the maximum distance from which a person can hear the pin drop. (This is the ideal maximum distance, but atmospheric absorption and other factors will make the actual maximum distance considerably smaller.)

Explanation / Answer

I would use the equations: P=Fv and I=P/(4pr^2) The second equation is the intensity (I) at a certain radius (r) We can assume that the intensity will be 0 at its maximum r, so your left with: 0=P/(4pr^2) You need to solve for P by using the equation P=Fv F is the force of the object v is the velocity of the object (its velocity as it hits the ground, which you need to solve for using kinematics) Once you solve for the power, plug it into the equation: 0=P/(4pr^2) and solve for the radius

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