At t=0, the shape of a travelling pulse is given by
`y(x,0)=(4xx10^(-3))/(8-(x)^(-2)`
where x and y are in metres. The wave function for the travelling pulse if the velocity of propagation is `5 m//s` in the x direction is given by

Options

A. `y(x,t)=(4xx10^(-3))/(8-(x^(2)-5t))`
B. `y(x,t)=(4xx10^(-3))/(8-(x-5t)^(2))
C. `y(x,t)=(4xx10^(-3))/(8-(x+5t)^(2))`
D. `y(x,t)=(4xx10^(-3))/(8-(x^(2)+5t))`

Explanation

To find the wave function for the given traveling pulse, we can follow these steps:

### Step 1: Understand the given pulse shape
At \( t = 0 \), the shape of the traveling pulse is given by:
\[ y(x, 0) = \frac{4 \times 10^{-3}}{8 - x^2} \]
This equation describes the initial shape of the wave.

### Step 2: Identify the wave propagation direction
The problem states that the wave is traveling in the positive x-direction with a velocity \( v = 5 \, \text{m/s} \). For a wave traveling in the positive x-direction, the general form of the wave function is:
\[ y(x, t) = f(x - vt) \]
where \( f \) is the shape of the wave at \( t = 0 \).

### Step 3: Substitute the velocity into the wave function
Since the wave is traveling in the positive x-direction, we replace \( vt \) with \( 5t \):
\[ y(x, t) = f(x - 5t) \]

### Step 4: Rewrite the initial pulse shape in terms of the wave function
We can express the wave function at any time \( t \) as:
\[ y(x, t) = \frac{4 \times 10^{-3}}{8 - (x - 5t)^2} \]

### Step 5: Finalize the wave function
Thus, the wave function for the traveling pulse is:
\[ y(x, t) = \frac{4 \times 10^{-3}}{8 - (x - 5t)^2} \]