The equation of a plane progressive wave is given by
`y=2sin(100pit-(pix)/(20))`
where x and y are in cm and t is in second. The amplitude and the initial phase of the wave are respectively.

Options

A. 2 cm and zero-radian
B. 1 cm and `pi`-radian
C. 2 cm and `pi`-radian
D. 2 cm and `(pi)/(2)` radian

Answer

To solve the problem, we need to analyze the given equation of the plane progressive wave:

\[ y = 2 \sin(100 \pi t - \frac{\pi x}{20}) \]

We will compare this equation with the standard form of a wave equation:

\[ y = A \sin(\omega t - kx + \phi) \]

where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number,
- \( \phi \) is the initial phase.

### Step 1: Identify the Amplitude
From the given equation, we can see that the coefficient of the sine function is \( 2 \). This coefficient represents the amplitude \( A \).

**Solution:**
\[ A = 2 \, \text{cm} \]

### Step 2: Identify the Initial Phase
Next, we need to determine the initial phase \( \phi \). In the standard wave equation, if there is no additional term added to the sine function (i.e., if it is just \( \sin(\text{something}) \)), then the initial phase \( \phi \) is \( 0 \).

**Solution:**
\[ \phi = 0 \]

### Final Answer
Thus, the amplitude and the initial phase of the wave are:
- Amplitude: \( 2 \, \text{cm} \)
- Initial Phase: \( 0 \)