Electromagnetic Waves: Understanding Frequency, Wavelength, and Color
Question:
1) An electromagnetic wave source has a wavelength of 1 × 10-6 m. What is its frequency? Which type of electromagnetic radiation is it? If it's in the visible spectrum, what color is it?
2) An electromagnetic wave source has a frequency of 7.5 × 1014 Hz. What is its wavelength? Which type of electromagnetic radiation is it? If it's in the visible spectrum, what color is it?
3) An electromagnetic wave source is orbiting a stationary receiver on a circular orbit at a non-relativistic velocity. In the lab frame of the source, the emitted wavelength is 10. Will the observed wavelength of the receiver be shorter, longer, or similar to 20? Please explain your reasoning.
Answer:
The frequency of the electromagnetic wave with a wavelength of 1 × 10-6 m is 3 × 1014 Hz. It is visible light, and the color is red. The wavelength of the electromagnetic wave with a frequency of 7.5 × 1014 Hz is 4 × 10-7 m. It is also visible light, and the color is blue. The observed wavelength of the receiver orbiting a stationary electromagnetic wave source will be similar to 20.
Explanation:
Electromagnetic waves consist of oscillating electric and magnetic fields and can be described by their frequency and wavelength. Frequency is the number of complete oscillations per second, measured in hertz (Hz), and wavelength is the distance between two consecutive points in the wave, measured in meters (m).
The speed of light is approximately 3 × 10^8 m/s, denoted by c. The relationship between frequency, wavelength, and speed of light is given by c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.
Solving the Questions:
Question 1:
Given wavelength = 1 × 10-6 m.
Frequency can be calculated using the formula: ν = c / λ.
Substitute the values: ν = (3 × 10^8 m/s) / (1 × 10^-6 m) = 3 × 10^14 Hz.
Based on the frequency range, the electromagnetic radiation is visible light, and the color is red, as the wavelength corresponds to the red end of the spectrum.
Question 2:
Given frequency = 7.5 × 10^14 Hz.
Wavelength can be calculated using the formula: λ = c / ν.
Substitute the values: λ = (3 × 10^8 m/s) / (7.5 × 10^14 Hz) = 4 × 10^-7 m.
Based on the wavelength, the electromagnetic radiation is visible light, and the color is blue, as the wavelength corresponds to the blue end of the spectrum.
Question 3:
The observed wavelength of the receiver will be similar to 20. This is because the wavelength of the electromagnetic wave emitted by the source is independent of the motion of the receiver. The observed wavelength is determined by the source and remains constant regardless of the receiver's motion.
For further information on electromagnetic waves, frequency, wavelength, and color, visit: [Link to Source].