Final answer:
To calculate the cone's maximum speed and acceleration, use the angular frequency, which is 2π times the frequency, and the amplitude. The maximum speed is amplitude multiplied by angular frequency and maximum acceleration is amplitude multiplied by angular frequency squared.
Step-by-step explanation:
If the cone of a loudspeaker moves sinusoidally at 1.4 kHz with an amplitude of 3.5 μm, the cone's maximum speed and maximum acceleration can be calculated using the formulas for sinusoidal motion in terms of angular frequency (ω) and amplitude (A).
The angular frequency ω is 2π times the frequency, so ω = 2π × 1.4 × 10³ s⁻¹. The maximum speed (v_max) is the amplitude times the angular frequency, that is v_max = Aω. Substituting the given values, v_max = (3.5 × 10⁻¶ m)(2π × 1.4 × 10³ s⁻¹).
The maximum acceleration (a_max) is given by a_max = Aω². Therefore, a_max = (3.5 × 10⁻¶ m)(2π × 1.4 × 10³ s⁻¹)².
By performing these calculations, you can find the cone's maximum speed and maximum acceleration.