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Two sinusoidal waves in a string are def...

Two sinusoidal waves in a string are defined by the function `y_(1)=(2.00 cm) sin (20.0x-32.0t)` and `y_(2)=(2.00 cm) sin (25.0x-40.0t)` where `y_(1), y_(2)` and `x` are in centimetres and `t` is in seconds.
(a). What is the phase difference between these two waves at the point `x=5.00 cm` at `t=2.00 s ?`
(b) what is the positive `x` value closest to the original for which the two phase differ by `+_ pi at t=2.00 s?` (That os a location where the two waves add to zero.)

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AI Generated Solution

To solve the problem, we will break it down into two parts as per the question. ### Part (a): Finding the Phase Difference 1. **Identify the Wave Functions**: - Wave 1: \( y_1 = (2.00 \, \text{cm}) \sin(20.0x - 32.0t) \) - Wave 2: \( y_2 = (2.00 \, \text{cm}) \sin(25.0x - 40.0t) \) ...
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