Two waves passing through a region are represented by `y=(1.0cm) sin [(3.14 cm^(-1))x - (157s^(-1) x - (157s^(-1))t]`
and `y = (1.5 cm) sin [(1.57 cm^(-1))x- (314 s^(-1))t].` Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.

Explanation

To find the displacement of the particle at \( x = 4.5 \, \text{cm} \) and \( t = 5.0 \, \text{ms} \) due to two waves, we need to calculate the displacement from each wave and then sum them up.

### Step 1: Write down the equations of the waves
The two waves are given by:
1. \( y_1 = (1.0 \, \text{cm}) \sin [(3.14 \, \text{cm}^{-1})x - (157 \, \text{s}^{-1})t] \)
2. \( y_2 = (1.5 \, \text{cm}) \sin [(1.57 \, \text{cm}^{-1})x - (314 \, \text{s}^{-1})t] \)

### Step 2: Substitute the values into the first wave equation
...