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Name: John
Status: educator
Grade: 9-12
Location: IL
Country: N/A
Date: 2/1/2005


Question:
According to the superposition principle of waves, the amplitudes of two waves interfering in phase add to form a new wave whose amplitude is the sum of the two. If the wave energy goes as the square of the amplitude, this seems to imply that the new wave has more energy than the sum of the two original waves (for example two identical waves add to twice the amplitude of either to form a wave with 4 times the energy?) Where is the flaw in the logic here?


Replies:
The wave energy as a square of the amplitude could be the flaw. Or at least your means of applying it here.
_     _           _     _
/  \_/  \_   +  /  \_/  \_ =

_    _
/ l   /  l
    \_l   \_

(Best I can draw it, sorry.) the sum wave is now twice the amplitude (whether measured in voltage, power, or height of a fluid wave), and if you consider the area within it, you have got twice the internal volume. So if we are talking about something like water, where the displaced volume times the speed of the waves can be translated to a measure of power, you have only doubled one of the factors.

It is also important to consider phase and direction. in most cases where multiple waves wind up at the same location, they are crossing from one direction or another. Often enough, these extra waves cancel each other out for no power, due to traveling in opposite directions. (like 2 people jerking on a rope in opposite directions instead of jerking the same direction)

Ryan Belscamper



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