∙Consider electromagnetic waves propagating in air. (a)...

$\bullet$ Consider electromagnetic waves propagating in air. (a) Determine the frequency of a wave with a wavelength of (i) $5.0 \mathrm{km},$ (ii) $5.0 \mu \mathrm{m},$ (iii) 5.0 $\mathrm{nm}$ . (b) What is the wavelength (in meters and nanometers) of (i) gamma rays of frequency $6.50 \times 10^{21} \mathrm{Hz}$ , (ii) an AM station radio wave of frequency 590 $\mathrm{kHz} ?$

Key Concepts

Speed of Light

The speed of light is a fundamental constant in physics, approximately 3.00 × 10^8 m/s in vacuum and air. It represents the speed at which all electromagnetic waves travel and is crucial for linking the wavelength and frequency of these waves in the equation c = ?f.

Frequency-Wavelength Relationship

This concept explains the inverse relationship between the frequency and wavelength of an electromagnetic wave, as expressed in the equation c = ?f. It indicates that as the wavelength increases, the frequency decreases, and vice versa, which is fundamental for solving problems involving the determination of either property given the other.

Unit Conversion

Proper unit conversion is essential in electromagnetic wave calculations to maintain consistency in equations. Converting distances (e.g., from kilometers to meters, micrometers to meters, nanometers to meters) and frequencies (e.g., from kilohertz to hertz) ensures that all quantities are expressed in compatible units when applying the fundamental relation c = ?f.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays with very short wavelengths and high frequencies to radio waves with long wavelengths and low frequencies. Understanding this spectrum helps classify different types of electromagnetic waves and recognize their characteristic frequency and wavelength ranges.

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