A loudspeaker diaphragm is producing a sound for 2.2 s by moving back and forth in simple harmonic motion. The angular frequency of the motion is 3.95 x 104 rad/s. How many times does the diaphragm move back and forth?

The diaphragm moves back and forth 13830.56 times

Explanation:

For simple harmonic motion, the angular frequency is calculated by using the expression

ω=2πf

where f is the rotational frequency

Therefore,

ω = 2πf ⇒ f = ω/2π

⇒ f = (3.95*10⁴rad/s) / 2π rad

⇒ f = 6286.62 s⁻¹

Therefore, determining the amount times that the diaphragm moves back and forth is essentially determining the pendulum's cycle and this is determined by

cycle = f * t

cycle = (6286.62 s⁻¹) * (2.2 s)

cycle = 13830.56 times

This means that the loudspeaker's diaphragm moves 13830.56 times at the level of sound that it produces.