To determine which waves are found in the specified frequency range of [tex]\(4 \times 10^{14}\)[/tex] to [tex]\(7.5 \times 10^{14}\)[/tex] Hz, with the speed of light given as [tex]\(2.998 \times 10^8\)[/tex] m/s, we need to calculate the corresponding wavelengths for these frequencies. The formula to convert frequency ([tex]\(f\)[/tex]) to wavelength ([tex]\(\lambda\)[/tex]) is:
[tex]\[
\lambda = \frac{c}{f}
\][/tex]
where:
- [tex]\( \lambda \)[/tex] is the wavelength,
- [tex]\( c \)[/tex] is the speed of light [tex]\( (2.998 \times 10^8 \, m/s) \)[/tex], and
- [tex]\( f \)[/tex] is the frequency.
First, let’s calculate the wavelength for the lower bound frequency of [tex]\(4 \times 10^{14}\)[/tex] Hz:
[tex]\[
\lambda_{lower} = \frac{2.998 \times 10^8 \, m/s}{4 \times 10^{14} \, Hz} = 7.495 \times 10^{-7} \, m \approx 749.5 \, nm
\][/tex]
Next, let’s calculate the wavelength for the upper bound frequency of [tex]\(7.5 \times 10^{14}\)[/tex] Hz:
[tex]\[
\lambda_{upper} = \frac{2.998 \times 10^8 \, m/s}{7.5 \times 10^{14} \, Hz} = 3.997 \times 10^{-7} \, m \approx 399.7 \, nm
\][/tex]
The visible light spectrum ranges from approximately 380 nm to 750 nm. We need to check if our calculated wavelengths fall within this range:
- The wavelength for the lower bound frequency is approximately 749.5 nm.
- The wavelength for the upper bound frequency is approximately 399.7 nm.
Both of these wavelengths, 749.5 nm and 399.7 nm, fall within the visible light spectrum range of 380 nm to 750 nm. Therefore, the waves in this frequency range are indeed visible light.
Thus, the correct answer is:
C. visible light
