What is the wavelength of electromagnetic radiation that has a 60 Hz frequency?
The Correct Answer and Explanation is:
To calculate the wavelength of electromagnetic radiation, we use the formula:Speed of light=Frequency×Wavelength\text{Speed of light} = \text{Frequency} \times \text{Wavelength}Speed of light=Frequency×Wavelength
where:
- The speed of light (c) is a constant, approximately 3.00×108 m/s3.00 \times 10^8 \, \text{m/s}3.00×108m/s.
- Frequency (f) is given as 60 Hz.
- Wavelength (λ) is what we want to find.
Rearranging the equation to solve for wavelength:λ=cf\lambda = \frac{c}{f}λ=fc
Now, plug in the known values:λ=3.00×108 m/s60 Hz\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{60 \, \text{Hz}}λ=60Hz3.00×108m/sλ=5.00×106 m\lambda = 5.00 \times 10^6 \, \text{m}λ=5.00×106m
So, the wavelength of the electromagnetic radiation with a 60 Hz frequency is 5,000,000 meters, or 5,000 kilometers.
Explanation:
The relationship between the speed of light, frequency, and wavelength is a fundamental concept in wave theory, particularly for electromagnetic waves. The speed of light is a constant in a vacuum, and it’s a crucial factor in determining the wavelength for a given frequency. In this case, we’re dealing with a very low-frequency electromagnetic wave (since 60 Hz is quite low compared to the typical radio or light waves).
Electromagnetic waves with such a low frequency (like 60 Hz) correspond to long wavelengths, which is why the result is in the order of millions of meters. In practical terms, 60 Hz is the frequency of powerline electricity in many parts of the world, which operates at a very low frequency compared to other electromagnetic waves like visible light or microwaves.
