At t=0, a transverse wave pulse in a wire is described by the function `y=6//(x^(2)-3)` where x and y are in metres. The function y(x,t) that describes this wave equation if it is travelling in the positive x direction with a speed of `4.5 m//s` is

Options

A. `y=(6)/((x+4.5t)^(2)-3)`
B. `y=(6)/((x-4.5t)^(2)+3)`
C. `y=(6)/((x+4.5t)^(2)+3)`
D. `y=(6)/((x-4.5t)^(2)-3)`

Explanation

To find the function \( y(x, t) \) that describes the wave pulse traveling in the positive x direction with a speed of \( 4.5 \, \text{m/s} \), we start with the given wave pulse function at \( t = 0 \):

\[ y(x, 0) = \frac{6}{x^2 - 3} \]

### Step 1: Identify the wave speed and direction
The wave is traveling in the positive x direction with a speed \( v = 4.5 \, \text{m/s} \).

### Step 2: Write the general form of the wave function
For a wave traveling in the positive x direction, the wave function can be expressed as:

\[ y(x, t) = f(x - vt) \]

where \( f \) is the shape of the wave at \( t = 0 \) and \( vt \) is the distance traveled by the wave after time \( t \).

### Step 3: Substitute the initial wave function into the general form
Since we have the initial wave function \( y(x, 0) \), we can substitute \( x - vt \) into this function.

Given:

\[ f(x) = \frac{6}{x^2 - 3} \]

We replace \( x \) with \( x - vt \):

\[ y(x, t) = f(x - vt) = \frac{6}{(x - vt)^2 - 3} \]

### Step 4: Substitute the value of \( v \)
Now, we substitute \( v = 4.5 \, \text{m/s} \):

\[ y(x, t) = \frac{6}{(x - 4.5t)^2 - 3} \]

### Final Answer
Thus, the function \( y(x, t) \) that describes the wave pulse traveling in the positive x direction is:

\[ y(x, t) = \frac{6}{(x - 4.5t)^2 - 3} \]