The equation of a progressive wave is
`y=0.02sin2pi[(t)/(0.01)-(x)/(0.30)]`
here x and y are in metres and t is in seconds. The velocity of propagation of the wave is

Options

A. `300 m//s`
B. `30 m//s`
C. `400 m//s`
D. `40 m//s`

Explanation

To find the velocity of propagation of the wave given by the equation:

\[ y = 0.02 \sin\left(2\pi\left(\frac{t}{0.01} - \frac{x}{0.30}\right)\right) \]

we can follow these steps:

### Step 1: Identify the wave equation format
The general form of a progressive wave is given by:

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

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

### Step 2: Extract \( \omega \) and \( k \)
From the given equation, we can rewrite it to match the standard form:

\[ y = 0.02 \sin\left(2\pi \left(\frac{t}{0.01} - \frac{x}{0.30}\right)\right) \]

This can be expressed as:

\[ y = 0.02 \sin\left(\frac{2\pi t}{0.01} - \frac{2\pi x}{0.30}\right) \]

From this, we can identify:
- \( \omega = \frac{2\pi}{0.01} \)
- \( k = \frac{2\pi}{0.30} \)

### Step 3: Calculate \( \omega \) and \( k \)
Now, let's calculate \( \omega \) and \( k \):

1. Calculate \( \omega \):
\[ \omega = \frac{2\pi}{0.01} = 200\pi \, \text{rad/s} \]

2. Calculate \( k \):
\[ k = \frac{2\pi}{0.30} \approx \frac{2\pi}{0.30} = \frac{20\pi}{3} \, \text{rad/m} \]

### Step 4: Calculate the velocity of the wave
The velocity \( v \) of the wave is given by the formula:

\[ v = \frac{\omega}{k} \]

Substituting the values of \( \omega \) and \( k \):

\[ v = \frac{200\pi}{\frac{20\pi}{3}} = 200\pi \times \frac{3}{20\pi} \]

The \( \pi \) cancels out:

\[ v = \frac{200 \times 3}{20} = \frac{600}{20} = 30 \, \text{m/s} \]

### Conclusion
The velocity of propagation of the wave is:

\[ \boxed{30 \, \text{m/s}} \]

---