To determine the correct formula for finding the frequency of an electromagnetic wave, we need to recall the fundamental relationship between the speed of light, frequency, and wavelength.
The formula that relates these quantities is:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
where:
- [tex]\( f \)[/tex] is the frequency of the electromagnetic wave,
- [tex]\( c \)[/tex] is the speed of light in a vacuum, approximately [tex]\( 3 \times 10^8 \)[/tex] meters per second,
- [tex]\( \lambda \)[/tex] (lambda) is the wavelength of the electromagnetic wave.
Given the following options:
1. [tex]\( f = c - \lambda \)[/tex]
2. [tex]\( f = \frac{\lambda}{c} \)[/tex]
3. [tex]\( f = \lambda + c \)[/tex]
4. [tex]\( f = \frac{c}{\lambda} \)[/tex]
We need to identify the option that matches our formula.
- Option 1 states [tex]\( f = c - \lambda \)[/tex], which suggests subtracting the wavelength from the speed of light. This formula is incorrect because it does not correctly relate frequency, speed of light, and wavelength.
- Option 2 states [tex]\( f = \frac{\lambda}{c} \)[/tex], which suggests dividing the wavelength by the speed of light. This is incorrect because it inverts the relationship we need; instead of dividing the speed of light by wavelength, it mistakenly divides wavelength by the speed of light.
- Option 3 states [tex]\( f = \lambda + c \)[/tex], which suggests summing the wavelength with the speed of light. This formula is incorrect for the same reason as the subtraction formula; it does not represent the correct physical relationship between these quantities.
- Option 4 states [tex]\( f = \frac{c}{\lambda} \)[/tex], which matches our established relationship. This is the correct formula, indicating that frequency is equal to the speed of light divided by the wavelength.
Therefore, the correct formula for finding the frequency of an electromagnetic wave is:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
Hence, the answer is:
[tex]\[ \boxed{4} \][/tex]
