Final answer:
The wave number can be calculated using the formula k = 2π / λ, where λ is the wavelength. By finding the wavelength using v = fλ, we can determine the wave number. For the given frequencies of 4×10^14 Hz and 5×10^16 Hz, the wave numbers are approximately 8.38×10^6 m^-1 and 1.05×10^9 m^-1, respectively.
Step-by-step explanation:
The wave number (k) of a wave can be calculated using the formula:
k = 2π / λ
where λ is the wavelength of the wave. To find the wave number, we first need to determine the wavelength using the formula:
v = fλ
where v is the velocity of the wave and f is the frequency. Using the given frequencies of 4×10^14 Hz and 5×10^16 Hz, we can calculate the wavelengths, and then use those values to find the wave numbers.
For the frequency of 4×10^14 Hz:
- Velocity of light (v) = 3×10^8 m/s
- Frequency (f) = 4×10^14 Hz
- Wavelength (λ) = v / f = (3×10^8 m/s) / (4×10^14 Hz) = 7.5×10^-7 m
Using the obtained wavelength, we can now calculate the wave number:
- Wave number (k) = 2π / λ = (2π) / (7.5×10^-7 m) ≈ 8.38×10^6 m^-1
Similarly, for the frequency of 5×10^16 Hz:
- Frequency (f) = 5×10^16 Hz
- Wavelength (λ) = v / f = (3×10^8 m/s) / (5×10^16 Hz) = 6×10^-9 m
Wave number (k) = 2π / λ = (2π) / (6×10^-9 m) ≈ 1.05×10^9 m^-1