Part A
The vibration of the speaker causes simple harmonic motion. The formula for calculating the maximum speed, vmax is expressed as
vmax = wA
where
w = angular speed
A = amplitude
Recall,
w = 2 x pi x f
where
f = frequency
pi is a constant whose value is 3.14
From the information given,
f = 1.8 KHz
we would convert from KHz to Hz
Recall,
1 KHz = 1 x 10^3 Hz
1.8 KHz = 1.8 x 10^3 Hz
By substituting the values into the formula, we have
w = 2 x 3.14 x 1.8 x 10^3
Also,
A = 4.5 μm
We would convert from μm to m
Recall,
1 μm = 1 x 10^-6 m
Thus,
4.5μm = 4.5 x 10^-6m
By substituting w = 2 x 3.14 x 1.8 x 10^3 and A = 4.5 x 10^-6 into vmax = wA, we have
vmax = 2 x 3.14 x 1.8 x 10^3 x 4.5 x 10^-6
vmax = 0.051 m/s
Part B
The formula for calculating max acceleration, Amax is
Amax = w^2A
By substituting w = 2 x 3.14 x 1.8 x 10^3 and A = 4.5 x 10^-6 into the formula, we have
Amax = (2 x 3.14 x 1.8 x 10^3)^2 x 4.5 x 10^-6
Amax = 575 m/s^2