Two waves are described by the equations: y 1 = A cos ⁡ 0.5 π x - 100 π t And y 2 = A cos ⁡ 0.46 π x - 92 π t Here x and y are in m and t is in s . Find the number of times y 1 + y 2 becomes zero per second, at x = 0 .

Question

Two waves are described by the equations: y 1 = A cos ⁡ 0.5 π x - 100 π t And y 2 = A cos ⁡ 0.46 π x - 92 π t Here x and y are in m and t is in s . Find the number of times y 1 + y 2 becomes zero per second, at x = 0 ., 46, 48, 192, 100

MARKS App · Accepted Answer

At x = 0 , y = y 1 + y 2 = 2 A cos ⁡ 96 π t cos ⁡ 4 π t Frequency of cos ⁡ 96 π t = 48 H z and that of cos ⁡ ( 4 π t ) function is 2 Hz In one-second cos function becomes zero at 96 times and second at 4 times. Hence net y will become zero 100 times in 1 second.

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