Asked by Lola
When responding to sound, the human eardrum vibrates about its equilibrium position. Suppose an eardrum is vibrating with an amplitude of 5.60 10-7 m and a maximum speed of 2.82 10-3 m/s.
I don't see how A and a, is given. =/
I don't see how A and a, is given. =/
Answers
Answered by
Lola
Damon, help me!!! =(
Answered by
Damon
harmonic motion with w = 2 pi *frequency or 2 pi/period
y = A sin w t
dy/dt = v = A w cos w t
d^2y/dt^2 = a = -A w^2 sin wt = -w^2 y
here
v max = Aw = 2.82*10^-3
and A = 5.6*10^-7
so
w = 2 pi f = 2 pi/T = 2.82/5.6 * 10^4
= .504*10^4 = 5040 radians/s
f = 5040/2pi = 801 Hz
T = 1/f = .00125 seconds
etc etc etc
y = A sin w t
dy/dt = v = A w cos w t
d^2y/dt^2 = a = -A w^2 sin wt = -w^2 y
here
v max = Aw = 2.82*10^-3
and A = 5.6*10^-7
so
w = 2 pi f = 2 pi/T = 2.82/5.6 * 10^4
= .504*10^4 = 5040 radians/s
f = 5040/2pi = 801 Hz
T = 1/f = .00125 seconds
etc etc etc
Answered by
Damon
oh
max acceleration magnitude = A w^2
= 5.6*10^-7 * (5040)^2
max acceleration magnitude = A w^2
= 5.6*10^-7 * (5040)^2
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