A plane electromagnetic wave of frequency 40 MHz travels in free space in the x-direction. At so

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A plane electromagnetic wave of frequency 40 MHz travels in...

A plane electromagnetic wave of frequency $40 \mathrm{MHz}$ travels in free space in the $x$-direction. At some point and at some instant, the electric field $\vec{E}$ has its maximum value of $750 \mathrm{~N} / \mathrm{C}$ in $y$-direction. The wavelength of the wave is (A) $3.5 \mathrm{~m}$ (B) $5.5 \mathrm{~m}$ (C) $7.5 \mathrm{~m}$ (D) $9.5 \mathrm{~m}$

A plane electromagnetic wave of frequency $40 \mathrm{MHz}$ travels in free space in the $x$-direction. At some point and at some instant, the electric field $\vec{E}$ has its maximum value of $750 \mathrm{~N} / \mathrm{C}$ in $y$-direction. The wavelength of the wave is
(A) $3.5 \mathrm{~m}$
(B) $5.5 \mathrm{~m}$
(C) $7.5 \mathrm{~m}$
(D) $9.5 \mathrm{~m}$

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Key Concepts

Frequency-Wavelength Relationship

The frequency-wavelength relationship is a fundamental concept in wave theory that relates the wavelength of a wave to its frequency and propagation speed. The basic formula is wavelength = speed / frequency. This relation shows that for a constant propagation speed (such as the speed of light in free space), an increase in frequency implies a decrease in wavelength, and vice versa.

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. They are characterized by their ability to travel in a vacuum, and their electric and magnetic field components are perpendicular to each other as well as to the direction of propagation. Their behavior is described by Maxwell's equations, and they cover a wide range of frequencies, including radio, microwave, infrared, visible, ultraviolet, X-rays, and gamma rays.

Speed of Light in Free Space

The speed of light in free space is a universal constant commonly denoted by 'c', approximately 3 x 10^8 meters per second. This constant is a critical factor in the propagation of electromagnetic waves in vacuum, linking the electric and magnetic field oscillations to the wavelength and frequency of the wave, and is central to the theories of electromagnetism and relativity.

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