The wave function (in SI unit) for a light wave is given as `Psi(x,t) = 10^(3) sinpi(3 xx 10^(6) x - 9 xx 10^(14)t)`.
The frequency of the wave is equal to

Options

A. `4.5 xx 10^(14) Hz`
B. `3.5 xx 10^(14) Hz`
C. `3.5 xx 10^(10) Hz`
D. `2.5 xx 10^(10) Hz`

Explanation

To find the frequency of the light wave given by 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 format
The general form of a wave function is given by:
\[ \Psi(x, t) = A \sin(kx - \omega t) \]
where:
- \( A \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency.

### Step 2: Compare with the given wave function
From the given wave function:
\[ \Psi(x, t) = 10^{3} \sin(\pi(3 \times 10^{6} x - 9 \times 10^{14} t)) \]
we can identify:
- \( k = \pi \times 3 \times 10^{6} \)
- \( \omega = \pi \times 9 \times 10^{14} \)

### Step 3: Extract the angular frequency
From our comparison, we find:
\[ \omega = 9 \times 10^{14} \pi \]

### Step 4: Relate angular frequency to frequency
The relationship between angular frequency \( \omega \) and frequency \( f \) is given by:
\[ \omega = 2\pi f \]
We can rearrange this to find \( f \):
\[ f = \frac{\omega}{2\pi} \]

### Step 5: Substitute the value of \( \omega \)
Substituting the value of \( \omega \):
\[ f = \frac{9 \times 10^{14} \pi}{2\pi} \]

### Step 6: Simplify the expression
The \( \pi \) in the numerator and denominator cancels out:
\[ f = \frac{9 \times 10^{14}}{2} \]
Calculating this gives:
\[ f = 4.5 \times 10^{14} \text{ Hz} \]

### Final Answer
Thus, the frequency of the wave is:
\[ f = 4.5 \times 10^{14} \text{ Hz} \]

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