The wave function (in `S.I unit`) for an electromagnetic wave is given as- `psi(x,t)=10^(3)sinpi(3xx10^(6)x-9xx10^(14)t)`
The speed of the wave is

Options

A. `9xx10^(14)m//s`
B. `3xx10^(8)m//s`
C. `3xx10^(6)m//s`
D. `3xx10^(7)m//s`

Explanation

To find the speed of the electromagnetic wave given the wave function \(\psi(x,t) = 10^3 \sin(\pi(3 \times 10^6)x - 9 \times 10^{14}t)\), we can follow these steps:

### Step 1: Identify the wave function parameters
The wave function is in the form:
\[ \psi(x,t) = A \sin(kx - \omega t) \]
where:
- \(A\) is the amplitude,
- \(k\) is the wave number,
- \(\omega\) is the angular frequency.

From the given wave function, we can identify:
- \(k = \pi \times 3 \times 10^6\)
- \(\omega = \pi \times 9 \times 10^{14}\)

### Step 2: Calculate the wave number \(k\) and angular frequency \(\omega\)
From the wave function:
- \(k = 3 \times 10^6 \, \text{m}^{-1}\)
- \(\omega = 9 \times 10^{14} \, \text{s}^{-1}\)

### Step 3: Use the relationship between speed, wave number, and angular frequency
The speed \(c\) of the wave can be calculated using the formula:
\[ c = \frac{\omega}{k} \]

### Step 4: Substitute the values of \(\omega\) and \(k\)
Substituting the values we found:
\[ c = \frac{9 \times 10^{14}}{3 \times 10^6} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ c = 3 \times 10^8 \, \text{m/s} \]

### Final Answer
The speed of the electromagnetic wave is:
\[ c = 3 \times 10^8 \, \text{m/s} \]

---