Two sinusoidal waves combining in a medium are described by the wave functions
`y_(1) = ( 3.0 cm) sin pi ( x + 0.60 t)`
`y_(2) = ( 3.0 cm) sin pi ( x - 0.60 t)`
where `x` is in centimeters and `t` is in seconds . Determine the maximum transverse position of an element of the medium at (a) ` x = 0.250 cm` , (b) `x = 0.500 cm` and (c ) `x = 1.50 cm`. (d) Find the three smallest values of `x` corresponding to antinodes.

Explanation

To solve the problem, we need to combine the two sinusoidal wave functions and then evaluate the resulting wave function at the specified positions. Let's go through the steps systematically.

### Step 1: Combine the Wave Functions
The two wave functions are given as:
- \( y_1 = (3.0 \, \text{cm}) \sin(\pi (x + 0.60 t)) \)
- \( y_2 = (3.0 \, \text{cm}) \sin(\pi (x - 0.60 t)) \)

Using the principle of superposition, we can combine these two waves:
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