An opera singer sings a note at a frequency of 250 Hz. It causes a nearby microphone diaphragm to vibrate at the same frequency with an amplitude of 0.2 mm.
(a) What is the angular frequency of the oscillations of the diaphragm?
(b) (i) Write an equation for the displacement of the diaphragm as a function of time. (You may assume that at t=0, the displacement is zero.) (ii) Hence, determine the displacement of the diaphragm at t=1.0 ms.
(c) (i) Write an equation for the velocity of the diaphragm as a function of time. (ii) Hence, determine the velocity of the diaphragm at t=1.0 ms. (iii) What is the maximum speed of the diaphragm?
(d) (i) Write an equation for the acceleration of the diaphragm as a function of time. (ii) Hence determine the acceleration of the diaphragm at t=1.0 ms. (iii) What is the maximum acceleration of the diaphragm?