A loudspeaker diaphragm is vibrating in simple harmonic motion with a frequency of 760 Hz and a maximum displacement of 0.85 mm.

(a) What is the angular frequency?

(b) What is the maximum speed?

(c) What is the maximum acceleration?

Answer: (a) 4775.2Hz (b) 4.06m/s (c) 19382.15m/s²

Explanation: Given that the frequency of oscilation f, is 760Hz and the maximum displacement x, is 0.85mm = 0.00085m

(a) Angular frequency w = 2πf

w = 2π * 760 = 4775.2Hz

(b) Maximum speed v is given as the product of angular frequency and maximum displacement

V=wx

V = 4775.2 * 0.00085

V = 4.06m/s

(c) The maximum acceleration a

= w²x

= (4775.2) ² * (0.00085)

a = 19382.15m/s².