The equation of progressive wave is `y = 0.2 sin 2pi``[(t)/(0.01)-(x)/(0.3)]`, where x and y are in metre and t is in second. The velocity of propagation of the wave is

Options

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

Explanation

To find the velocity of propagation of the wave given by the equation \( y = 0.2 \sin \left( 2\pi \left( \frac{t}{0.01} - \frac{x}{0.3} \right) \right) \), we can follow these steps:

### Step 1: Identify the wave equation format
The general form of a progressive wave can be expressed as:
\[ y = A \sin \left( \frac{2\pi}{T} t \pm \frac{2\pi}{\lambda} x \right) \]
where:
- \( A \) is the amplitude,
- \( T \) is the time period,
- \( \lambda \) is the wavelength.

### Step 2: Extract parameters from the given equation
From the given wave equation:
\[ y = 0.2 \sin \left( 2\pi \left( \frac{t}{0.01} - \frac{x}{0.3} \right) \right) \]
we can identify:
- The time period \( T = 0.01 \) seconds,
- The wavelength \( \lambda = 0.3 \) meters.

### Step 3: Use the wave velocity formula
The velocity \( v \) of a wave is given by the formula:
\[ v = \frac{\lambda}{T} \]

### Step 4: Substitute the values
Now substituting the identified values into the formula:
\[ v = \frac{0.3 \, \text{m}}{0.01 \, \text{s}} = 30 \, \text{m/s} \]

### Conclusion
Thus, the velocity of propagation of the wave is:
\[ \boxed{30 \, \text{m/s}} \]

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