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In a loudspeaker, an electromagnetic coil rapidly drives a paper cone back and forth, sending out sound waves.Part AIf the cone of a loudspeaker moves sinusoidally at 1.6 kHz with an amplitude of 2.5 μm, what is the cone's maximum speed?Part BWhat is the cone's maximum acceleration?

User Akka Jaworek
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1 Answer

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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

User Byungwook
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