

Wave Energy
Name: John
Status: educator
Grade: 912
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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Update: June 2012

