Homework at the Speed of Light and Sound

1. A lightning bolt releases a thunderclap as it discharges. You see the bolt almost immediately, but it takes longer (five seconds per mile) for the force of the sound to propagate through the air to your ears. Note that lightning, being electricity, of course travels at the speed of light. It generates continuous booms as it rips through the atmosphere faster than the speed of sound; this creates overpressures that move the air very quickly and create shock waves. Consider the relative speeds involved: If you see thundercloud lightning strike a tree, where does the first boom you hear come from?

2. Similarly, a fighter jet flies above you at supersonic speed. You see the jet as it passes over your head, followed by the roar of the jets a few seconds later (exactly the same sonic boom effect as the lightning bolt). It is pushed forward by a series of massive explosions but is traveling faster than those explosions are able to expand through the air and reach your ears. Note that the force has mostly dissipated by the time it reaches you, leaving you with only a sound instead of the explosive force of the engine exhaust. What would happen if the fighter pilot dropped an unguided bomb as he was passing over your head? What about if he fired a missile forward?

3. Vibration of any kind is also a decent thought experiment. Imagine striking a drum while resting your hand on the skin. You can feel the vibration of the drum as the energy of the strike moves through the material. You can hear the dull sound of the drum beat as that energy rebounds in the resonator and through the air to vibrate your eardrums*. Does the sound cease before, after, or simultaneously with the vibration in your hands? What would be the implications of the skin vibrating slower, faster, or at the same speed as sound? What would be differences between hitting a drum and striking a steel pipe against the ground?

*Extra Credit: Consider that our hearing is based upon our brain's interpretation of vibrations in our sensitive eardrum. Though we experience it quite differently, it is a sensation that is functionally similar to blowing on your arm. And yet there are many limitations on hearing. Things can be too quiet or too high-pitched, and it is difficult to hear through solid objects like doors. Our ears are tuned precisely to the sound energy traveling the air we are surrounded with. If we lived in a more heavily oxygenated atmosphere, like during the Cretaceous Period when Tyrannosaurus Rex walked the Earth, the thicker atmosphere would necessitate a different tuning to a faster "speed of sound".