Summary
Highlights
A second problem involves calculating the frequency of a radio wave with a wavelength of 0.52 meters. Using the same formula f = c/λ, and the constant c, the frequency is calculated as 5.77 x 10^8 Hertz.
A quick recap of electromagnetic waves, including their definition, properties, and the seven types (radio, microwave, infrared, visible light, ultraviolet, X-rays, and gamma rays). These are arranged on the electromagnetic spectrum where wavelength decreases and frequency increases from radio waves to gamma rays. This module focuses on solving problems involving wavelength, frequency, and energy of EM waves.
Frequency (f) is the number of cycles or vibrations in one unit of time, typically seconds, and is expressed in Hertz (Hz). Energy (E) is the capacity to do work, symbolized by E and expressed in Joules (J). Wavelength (λ) is the distance between corresponding points of two consecutive waves (e.g., two crests or two troughs), symbolized by the Greek letter lambda and expressed in meters (m).
Two key constants are introduced: the speed of light in vacuum (c), which is 3 x 10^8 meters per second, and Planck's constant (h), which is 6.63 x 10^-34 Joule-seconds. The speed of light is a constant value to be used in calculations, and Planck's constant requires careful handling due to its small value.
The first equation discussed is c = λf, where c is the speed of light, λ is the wavelength in meters, and f is the frequency in Hertz. Since c is a constant, problems will typically ask for either wavelength or frequency. A triangular mnemonic tool is demonstrated to easily derive formulas for λ (λ = c/f) or f (f = c/λ).
The first sample problem asks for the frequency of an electromagnetic wave with a wavelength of 150 meters. The constant c (3 x 10^8 m/s) and the given wavelength (λ = 150 m) are used in the derived formula f = c/λ. The solution involves substituting these values and calculating the frequency, which is 2 x 10^6 Hertz.
The third problem shifts to finding the wavelength when the frequency is given as 8.0 x 10^14 Hertz. Using the derived formula λ = c/f, and the constant c, the wavelength is calculated to be 3.75 x 10^-7 meters.
A practice problem is presented: an FM radio station broadcasts at a frequency of 107.9 Hertz, and the task is to find the wavelength of the radio signal. The video pauses for viewers to solve it. Using λ = c/f, with c = 3 x 10^8 m/s and f = 107.9 Hz, the calculated wavelength is 2.78 x 10^6 meters.