Part A
The sound generated moves back and forth in simple harmonic motion. The formula for calculating maximum speed, vmax is expressed as
vmax = wA
where
w is the angular velocity
A is the amplitude
Recall,
w = 2 x pi x frequency
Thus,
vmax = 2 x pi x frequency x amplitude
From the information given,
frequency = 1.6KHz
We would convert from KHz to Hz
Recall,
1 KHz = 1 x 10^3 Hz
1.6 KHz = 1.6 x 10^3 Hz
amplitude = 2.5 μm
we would convert μm to m
Recall,
1 μm = 1 x 10^-6 m
2.5 μm = 2.5 x 10^-6 m
pi = 3.14
By substituting these values into the formula, we have
vmax = 2 x 3.14 x 1.6 x 10^3 x 2.5 x 10^-6
vmax = 0.025 m/s
Part B
The formula for calculating maximum acceleration, Amax is
Amax = w^2A
where
a = amplitude
Amax = (2 x pi x frequency)^2A
Amax = (2 x 3.14 x 1.6 x 10^3)^2 x 2.5 x 10^-6
Amax = 252.4 m/s^2