Certainly! To find the wavelength of a microwave given its frequency and the speed of light, we'll use the fundamental relationship between speed, frequency, and wavelength in wave mechanics.
The relationship is given by the formula:
[tex]\[ \text{wavelength} (\lambda) = \frac{\text{speed of light} (c)}{\text{frequency} (f)} \][/tex]
Given:
- The frequency, [tex]\( f = 2.45 \times 10^9 \)[/tex] Hz
- The speed of light, [tex]\( c = 3.0 \times 10^8 \)[/tex] m/s
Now, we'll substitute these values into the formula to calculate the wavelength:
[tex]\[ \lambda = \frac{c}{f} \][/tex]
[tex]\[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{2.45 \times 10^9 \, \text{Hz}} \][/tex]
Dividing the numerical values:
[tex]\[ \lambda = \frac{3.0}{2.45} \times 10^{8-9} \, \text{m} \][/tex]
[tex]\[ \lambda = 1.2244897959183673 \times 10^{-1} \, \text{m} \][/tex]
Converting [tex]\(1.2244897959183673 \times 10^{-1} \, \text{m}\)[/tex] to standard notation:
Hence, the wavelength of the microwave is:
[tex]\[ \lambda \approx 0.122 \, \text{m} \][/tex]
This result expresses the wavelength of a microwave with a frequency of [tex]\(2.45 \times 10^9\)[/tex] Hz, when the speed of light is [tex]\(3.0 \times 10^8\)[/tex] m/s.
