A loudspeaker diaphragm is producing a sound for 2.0 s by moving back and forth in a simple harmonic motion. The angular frequency of the motion is 8.55 104 rad/s. How many times does the diaphragm move back and forth?

To find the number of times the diaphragm moves back and forth, we need to determine the period of the motion.

The period of a simple harmonic motion is the time taken for one complete cycle or one back and forth motion. It is given by the formula:

T = (2π) / ω

Where T is the period and ω is the angular frequency.

Given that the angular frequency is 8.55 × 10^4 rad/s, we can substitute this value into the equation:

T = (2π) / (8.55 × 10^4)

Calculating this gives us:

T ≈ 7.35 × 10^-5 s

Now, we need to find out how many periods occur in the 2.0 s duration. We can divide the total time (2.0 s) by the period (T) to get the number of periods:

Number of periods = Total time / Period

Number of periods = 2.0 s / 7.35 × 10^-5 s

Calculating this gives us:

Number of periods ≈ 2.72 × 10^4

Therefore, the diaphragm moves back and forth approximately 2.72 × 10^4 times in the given time of 2.0 seconds.