Three sinusodal waves having amplitudes a, a/2 and a/3 are superposed. They have the same period and thelr phase are 0, `pi//2` and respectively. Find (i) The resultant amplitude and phase (ii) Draw a sketch to show the resultant wave.

Explanation

To solve the problem of three sinusoidal waves having amplitudes \( a \), \( \frac{a}{2} \), and \( \frac{a}{3} \) with phases \( 0 \), \( \frac{\pi}{2} \), and \( \pi \) respectively, we will follow these steps:

### Step 1: Write the equations of the waves
The three waves can be expressed as:
1. \( y_1 = a \sin(\omega t - kx) \)
2. \( y_2 = \frac{a}{2} \sin\left(\omega t - kx + \frac{\pi}{2}\right) \)
3. \( y_3 = \frac{a}{3} \sin(\omega t - kx + \pi) \)

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