1. Find the wavelength (in m) of light that has a frequency of 892 MHz.
The speed of light in a vacuum is approximately 2.998 × 10^8 meters per second (m/s).
The formula relating the speed of light, wavelength, and frequency is:
c = λν
Where:
c = speed of light (m/s)
λ = wavelength (m)
ν = frequency (Hz)
To find the wavelength, we rearrange the formula:
λ = c / ν
Given:
Frequency (ν) = 892 MHz = 892 × 10^6 Hz
Plugging in the values:
λ = (2.998 × 10^8 m/s) / (892 × 10^6 Hz)
Simplifying:
λ = 2.998 × 10^8 / 892 × 10^6
= 2.998 / 892 × 10^2
≈ 3.36 × 10^-4 m
Therefore, the wavelength of light with a frequency of 892 MHz is approximately 3.36 × 10^-4 meters.
2. Find the frequency (in Hz) of light that has a wavelength of 77 cm.
Again, we'll use the formula:
c = λν
Rearranging the formula to solve for the frequency:
ν = c / λ
Given:
Wavelength (λ) = 77 cm = 77 × 10^-2 m (converting cm to meters)
Plugging in the values:
ν = (2.998 × 10^8 m/s) / (77 × 10^-2 m)
Simplifying:
ν = 2.998 × 10^8 / 77 × 10^-2
= 2.998 / 77 × 10^10
≈ 3.89 × 10^9 Hz
Therefore, the frequency of light with a wavelength of 77 cm is approximately 3.89 × 10^9 Hz.