Paragraph: Two plane harmonic sound waves are expressed by the equations. aligned & y₁(x, t)=A (0.5 x-100 t) & y₂(x, t)=A (0.46 x-92 t) aligned (All parameters are in MKS) Question: At x=0 how many times the amplitude of y₁+y₂ is zero in one second at x=0 ?

Step-by-step solution

At x=0, y=y₁+y₂=2 A 96 t 4 t Frequency of (96 t) function is 48 ~Hz and that of (4 t) function is 2 ~Hz . In one second cos function becomes zero at 2 f times, where f is the frequency. Therefore, first function will become zero at 96 times and the second at 4 times. But second overlaps with first. Hence, net y will become zero 96 times in 1 second.