A transverse wave travelling on a stretched string is is represented by the equation
`y =(2)/((2x - 6.2t)^(2)) + 20`. Then ,

Options

A. (a)velocity of the wave is `3.1m//s`
B. (b) amplitude of the wave is `0.1m`
C. (c)frequency of the wave is `20 Hz`
D. (d) wavelength of the wave is `1m`

Explanation

To solve the problem, we start with the given wave equation:

\[ y = \frac{2}{(2x - 6.2t)^2} + 20 \]

### Step 1: Identify the parameters from the wave equation

The standard form of a transverse wave is generally given as:

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

Where:
- \( A \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency,
- \( d \) is the vertical shift.

In our equation, we can identify:
- The term \( (2x - 6.2t) \) suggests that \( k = 2 \) and \( \omega = 6.2 \).

### Step 2: Calculate the amplitude

From the equation, we can see that the amplitude \( A \) can be derived from the term in the numerator:

\[ A = \frac{2}{20} = 0.1 \, \text{meters} \]

### Step 3: Calculate the velocity of the wave

The velocity \( v \) of the wave can be calculated using the formula:

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

Substituting the values we found:

\[ v = \frac{6.2}{2} = 3.1 \, \text{meters/second} \]

### Step 4: Calculate the frequency of the wave

The frequency \( f \) can be calculated using the relationship:

\[ f = \frac{\omega}{2\pi} \]

Substituting the value of \( \omega \):

\[ f = \frac{6.2}{2\pi} \approx 0.986 \, \text{Hertz} \]

### Step 5: Calculate the wavelength of the wave

The wavelength \( \lambda \) can be calculated using the formula:

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

Substituting the value of \( k \):

\[ \lambda = \frac{2\pi}{2} = \pi \, \text{meters} \approx 3.14 \, \text{meters} \]

### Summary of Results

- Velocity of the wave \( v = 3.1 \, \text{m/s} \)
- Amplitude \( A = 0.1 \, \text{m} \)
- Frequency \( f \approx 0.986 \, \text{Hz} \)
- Wavelength \( \lambda \approx 3.14 \, \text{m} \)

### Final Conclusion

Based on the calculations, the correct values are:
- Velocity: 3.1 m/s (Correct)
- Amplitude: 0.1 m (Correct)
- Frequency: Approximately 0.986 Hz (Not 20 Hz)
- Wavelength: Approximately 3.14 m (Not 1 m)