Question

An electromagnetic wave travelling in vacuum has its electric field component, $E=15\sin(1.57y+5.4t)\hat{j}$. The wavelength of the wave is:

• A. 4.0 m
• B. 3.0 m
• C. 2.5 m
• D. 2.0 m
• E. 1.0 m

Hint:

Recognize $1.57$ as $\pi/2$ to simplify calculations: $\lambda = 2\pi / (\pi/2) = 4$.

Answer 1

The Correct Option is A

Step 1: Concept
Compare the given equation with the standard wave equation $E = E_0 \sin(ky + \omega t)$.

Step 2: Analysis
From the equation, the wave vector $k = 1.57$.

Step 3: Calculation
The relationship between wavelength ($\lambda$) and wave vector is $k = \frac{2\pi}{\lambda}$.
$\lambda = \frac{2\pi}{1.57} \approx \frac{2 \times 3.14}{1.57} = \frac{6.28}{1.57} = 4.0$ m. Final Answer: (A)