Consider simultaneously running 500 dissimilar function generator loudspeaker systems, each of which produces a pure sine wave sound of the same amplitude. Oscillator one produces a pure 20 Hz sine wave, oscillator two produces a pure 40 Hz sine wave, oscillator three a pure 60 Hz sine wave ... oscillator 500 produces a pure 10000 Hz sine wave. At time t=0 all the oscillators are in phase.
a. Estimate the value of t for the first time after t=0 at which the volume of the resulting sound would be essentially 0.
b. Would the initial "relatively loud interval" ever repeat? If yes, with what period would it repeat and why? If not, why not?