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Waves y(1) = Acos(0.5pix - 100pit) and y...

Waves `y_(1) = Acos(0.5pix - 100pit)` and `y_(2)=Acos(0.46pix - 92pit)` are travelling along x-axis. (Here `x` is in `m` and `t` is in second)
(3) The number of times `y_(1) + y_(2) = 0` at `x = 0` in `1sec` is

A

100

B

46

C

192

D

96

Text Solution

Verified by Experts

The correct Answer is:
A
At `x = 0, y = y_(1) + y_(2)`
=`2A cos 96 pi t cos 4 pi t`
Freqency of `cos (96 pi t)` function is `48 Hz` and that of `cos (4 pi t)` function is `2 Hz`. In `1 s, 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 the first. Hence, net `y` will become zero `100` times in `1 s`.
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