Absolutely, let's solve this problem step by step.
1. Identify the given values:
- Frequency ([tex]\( \nu \)[/tex]) of the wave: [tex]\( 1.0 \times 10^6 \, \text{sec}^{-1} \)[/tex]
- Speed of light ([tex]\( c \)[/tex]): [tex]\( 3.0 \times 10^{10} \, \text{cm/s} \)[/tex]
2. Recall the formula to calculate wavelength ( [tex]\( \lambda \)[/tex] ):
- The wavelength is related to the speed of light and the frequency by the formula:
[tex]\[
\lambda = \frac{c}{\nu}
\][/tex]
3. Substitute the known values into the formula:
- Here, [tex]\( c = 3.0 \times 10^{10} \, \text{cm/s} \)[/tex] and [tex]\( \nu = 1.0 \times 10^6 \, \text{sec}^{-1} \)[/tex]
[tex]\[
\lambda = \frac{3.0 \times 10^{10} \, \text{cm/s}}{1.0 \times 10^6 \, \text{sec}^{-1}}
\][/tex]
4. Perform the division:
- When we divide [tex]\( 3.0 \times 10^{10} \)[/tex] by [tex]\( 1.0 \times 10^6 \)[/tex], we get:
[tex]\[
\lambda = 3.0 \times 10^4 \, \text{cm}
\][/tex]
5. Express the wavelength in the form of [tex]\( \lambda \times 10^3 \, \text{cm} \)[/tex]:
- We have [tex]\( 3.0 \times 10^4 \, \text{cm} \)[/tex], which can be expressed as [tex]\( 30 \times 10^3 \, \text{cm} \)[/tex].
Thus, the wavelength for the given wave is [tex]\( \boxed{30} \times 10^3 \, \text{cm} \)[/tex].
