- #1
DaydreamNation
- 17
- 1
I tried to come up with a simple calculus-free explanation for why the energy in a sound wave is proportional to the square of the wave's amplitude for my musical acoustics class. I think this makes sense, and seems to just be an elaboration of what Donald Hall writes, but I haven't seen it explained this way elsewhere so please let me know if there are some problems here.
If we use the SHM model and imagine a ball on a spring, A (amplitude) is the maximum displacement. To start the vibrating system, the ball must be displaced by A.
Then, how much work is done when starting the vibration?
W=Fd and d=A
F=ma
a=v/t
v=d/t
a=d/t2
F=md/t2
W=md2/t2 or mA2/t2
Energy transferred = work done
.˙. E is proportional to A2
If we use the SHM model and imagine a ball on a spring, A (amplitude) is the maximum displacement. To start the vibrating system, the ball must be displaced by A.
Then, how much work is done when starting the vibration?
W=Fd and d=A
F=ma
a=v/t
v=d/t
a=d/t2
F=md/t2
W=md2/t2 or mA2/t2
Energy transferred = work done
.˙. E is proportional to A2