Which of the following is not true for the progressive wave
`y=4sin2pi((t)/(0.02)-(x)/(100))`
where x and y are in cm and t in seconds.

Options

A. The amplitude is 4 cm
B. The wavelength is 100 cm
C. The frequency is 50 Hz
D. The velocity of propagation is `2 cm//s`

Explanation

To solve the problem, we need to analyze the given wave equation and extract the relevant parameters: amplitude, frequency, wavelength, and velocity. The wave equation provided is:

\[ y = 4 \sin\left(2\pi\left(\frac{t}{0.02} - \frac{x}{100}\right)\right) \]

### Step 1: Identify the Amplitude
The amplitude \( a \) is the coefficient in front of the sine function.

From the equation:
- Amplitude \( a = 4 \, \text{cm} \)

### Step 2: Identify the Frequency
The general form of the wave equation is:

\[ y = a \sin(2\pi f t - kx) \]

Where:
- \( f \) is the frequency
- \( k \) is the wave number

From the equation, we can see that:

\[ 2\pi f = \frac{1}{0.02} \]

To find the frequency \( f \):

\[ f = \frac{1}{0.02 \cdot 2\pi} = \frac{1}{0.02} = 50 \, \text{Hz} \]

### Step 3: Identify the Wavelength
The wave number \( k \) is given by:

\[ k = \frac{2\pi}{\lambda} \]

From the equation, we can see that:

\[ k = \frac{1}{100} \]

To find the wavelength \( \lambda \):

\[ \lambda = \frac{2\pi}{k} = 100 \, \text{cm} \]

### Step 4: Calculate the Velocity
The velocity \( v \) of the wave can be calculated using the formula:

\[ v = f \cdot \lambda \]

Substituting the values we found:

\[ v = 50 \, \text{Hz} \cdot 100 \, \text{cm} = 5000 \, \text{cm/s} \]

### Step 5: Evaluate the Options
Now we need to check the options provided in the question:

1. Amplitude is 4 cm (True)
2. Wavelength is 100 cm (True)
3. Frequency is 50 Hz (True)
4. Velocity of propagation is 2 cm/s (False)

### Conclusion
The statement that is not true is that the velocity of propagation is 2 cm/s. The correct velocity is 5000 cm/s.

### Final Answer
The option that is not true is: **Velocity of propagation is 2 cm/s.**

---