To find the frequency of a light wave given its wavelength, we use the relationship between the speed of light, frequency, and wavelength. The formula for this relationship is:
[tex]\[ \text{Frequency} = \frac{\text{Speed of light}}{\text{Wavelength}} \][/tex]
where:
- The speed of light ([tex]\( c \)[/tex]) is approximately [tex]\( 3.00 \times 10^8 \)[/tex] meters per second (m/s).
- The wavelength ([tex]\( \lambda \)[/tex]) is given as 3.50 meters (m).
Let's solve this step-by-step:
1. Write down the formula:
[tex]\[ \text{Frequency} = \frac{c}{\lambda} \][/tex]
2. Substitute the known values into the formula:
- [tex]\( c = 3.00 \times 10^8 \)[/tex] m/s
- [tex]\( \lambda = 3.50 \)[/tex] m
[tex]\[
\text{Frequency} = \frac{3.00 \times 10^8 \, \text{m/s}}{3.50 \, \text{m}}
\][/tex]
3. Perform the division:
[tex]\[
\text{Frequency} = \frac{3.00 \times 10^8}{3.50}
\][/tex]
[tex]\[
\text{Frequency} = 0.857 \times 10^8 \, \text{Hz}
\][/tex]
4. Convert the result to standard scientific notation:
[tex]\[
\text{Frequency} = 8.57 \times 10^7 \, \text{Hz}
\][/tex]
Thus, the frequency of the light wave with a wavelength of 3.50 meters is [tex]\( 8.57 \times 10^7 \)[/tex] Hz, not [tex]\( 1.20 \times 10^3 \)[/tex] Hz.
