The electric field part of an electromagnetic wave in vacuum is
`E=3.1(N)/(C)cos[(1.8("rad")/("m"))y+(5.4xx10^(8)("rad")/(s))t]hati`
The wavelength of this part of electromagnetic wave is

Options

A. 1.5 m
B. 2 m
C. 2.5 m
D. 3.5 m

Explanation

To find the wavelength of the given electromagnetic wave, we can follow these steps:

### Step-by-step Solution:

1. **Identify the given electric field equation**:
The electric field of the electromagnetic wave is given as:
\[ E = 3.1 \, \text{N/C} \cos\left(1.8 \, \text{rad/m} \cdot y + 5.4 \times 10^8 \, \text{rad/s} \cdot t\right) \hat{i} \]

2. **Compare with the standard form**:
The standard form of an electromagnetic wave can be expressed as:
\[ E = E_0 \cos(k y + \omega t) \]
where:
- \(E_0\) is the amplitude,
- \(k\) is the wave number,
- \(\omega\) is the angular frequency.

From the given equation, we can identify:
- \(E_0 = 3.1 \, \text{N/C}\)
- \(k = 1.8 \, \text{rad/m}\)
- \(\omega = 5.4 \times 10^8 \, \text{rad/s}\)

3. **Use the relationship between wave number and wavelength**:
The wave number \(k\) is related to the wavelength \(\lambda\) by the formula:
\[ k = \frac{2\pi}{\lambda} \]
Rearranging this gives:
\[ \lambda = \frac{2\pi}{k} \]

4. **Substitute the value of \(k\)**:
Now, substituting the value of \(k\) into the wavelength formula:
\[ \lambda = \frac{2\pi}{1.8} \]

5. **Calculate the wavelength**:
Using \( \pi \approx 3.14\):
\[ \lambda = \frac{2 \times 3.14}{1.8} \approx \frac{6.28}{1.8} \approx 3.49 \, \text{m} \]

### Final Answer:
Thus, the wavelength of the electromagnetic wave is approximately:
\[ \lambda \approx 3.49 \, \text{m} \]