Answer:
Approximately [tex]6.67 \times 10^{14}\; {\rm Hz}[/tex], assuming that the wavelength was measured in vacuum.
Explanation:
Let [tex]v[/tex] denote the speed of the wave, [tex]f[/tex] the frequency of the wave, and [tex]\lambda[/tex] the wavelength of this wave. It is given that [tex]v = \lambda\, f[/tex].
It is given that the wavelength of this light is [tex]\lambda = 450\; {\rm nm} = 4.50 \times 10^{-7}\; {\rm m}[/tex]. Assume that this wavelength is measured when the light beam is in vacuum, where the speed of light (wave speed) is [tex]v = c \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}[/tex].
Rearrange the equation [tex]v = \lambda\, f[/tex] to find the frequency [tex]f[/tex] of this wave:
[tex]\begin{aligned} f &= \frac{v}{\lambda} \\ &\approx \frac{3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}}{4.50 \times 10^{-7}\; {\rm m}} \\ &\approx 6.67 \times 10^{14}\; {\rm s^{-1}}\end{aligned}[/tex].
Note that [tex]1\; {\rm Hz}[/tex] is equivalent to [tex]1\; {\rm s^{-1}}[/tex]. Therefore, the frequency of this wave would be [tex]f \approx 6.67 \times 10^{14}\; {\rm Hz}[/tex].
