If at `t = 0`, a travelling wave pulse on a string is described by the function.
`y = (6)/(x^(2) + 3)`
What will be the waves function representing the pulse at time `t`, if the pulse is propagating along positive x-axis with speed `4m//s`?

Options

A. `y=(6)/(x+4t)^(2) +3`
B. `y=(6)/(x - 4t)^(2) +3`
C. `y =(6)/(x - t)^(2)`
D. `y =(6)/(x - t)^(2)+12`

Explanation

To solve the problem, we need to find the wave function representing the pulse at time `t`, given the initial wave function and the speed of propagation.

### Step-by-Step Solution:

1. **Identify the Initial Wave Function**:
The initial wave function at `t = 0` is given by:
\[ y = \frac{6}{x^2 + 3} \]

2. **Understand the Wave Propagation**:
The wave pulse is propagating along the positive x-axis with a speed of `4 m/s`. The general form of a wave function that travels in the positive x direction is:
\[ y(x, t) = f(x - vt) \]
where `v` is the speed of the wave.

3. **Determine the Wave Parameters**:
From the problem, we know:
- Speed \( v = 4 \, \text{m/s} \)
- The form of the wave function at `t = 0` can be compared to the general form.

4. **Identify the Wave Function Form**:
The wave function can be expressed as:
\[ y(x, t) = \frac{6}{(x - vt)^2 + 3} \]
Here, we need to replace \( v \) with `4 m/s`.

5. **Substituting the Speed**:
Substitute \( v \) into the equation:
\[ y(x, t) = \frac{6}{(x - 4t)^2 + 3} \]

6. **Final Wave Function**:
Therefore, the wave function representing the pulse at time `t` is:
\[ y(x, t) = \frac{6}{(x - 4t)^2 + 3} \]