At x=0,y=y1​+y2​=2Acos96πtcos4πtFrequency of cos(96πt) function is 48 Hz and that of cos(4πt) function is 2 Hz.In one second, cos function becomes zero at 2f times, where f is the frequency. Therefore, first function will become zero at 96 times and the second at 4 times. But second will not overlap with first. Hence, net y will become zero 100 times in 1s..NOTE First function will become zero, when96πt1​=(2π−1)2π​Similarly, second function will become zero, when4πt2​={2m−1)2π​If they overlap, then t1​=t2​⇒96π2n−1​=4π2m−1​ or 2m−12n−1​=24or an even number. But (2n−1) and (2m−1) both are odd number. So, their ratio can't be an even numbers. So they don't overlap.