Answered

Select the correct answer.

A light wave travels at a speed of [tex]3.0 \times 10^8[/tex] meters/second. If the wavelength is [tex]7.0 \times 10^{-7}[/tex] meters, what is the frequency of the wave?

A. [tex]2.5 \times 10^{-14}[/tex] hertz
B. [tex]4.3 \times 10^{14}[/tex] hertz
C. [tex]1.7 \times 10^{-14}[/tex] hertz
D. [tex]5.1 \times 10^{-14}[/tex] hertz



Answer :

To determine the frequency of the light wave, we can use the fundamental relationship between speed, frequency, and wavelength, which is given by the equation:

[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]

Here, we are given the speed of light and the wavelength:

- Speed of light, [tex]\( c = 3.0 \times 10^8 \)[/tex] meters/second
- Wavelength, [tex]\( \lambda = 7.0 \times 10^{-7} \)[/tex] meters

We need to solve for the frequency [tex]\( f \)[/tex]. Rearranging the equation to solve for frequency, we get:

[tex]\[ f = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]

Substituting the given values into the equation:

[tex]\[ f = \frac{3.0 \times 10^8 \text{ m/s}}{7.0 \times 10^{-7} \text{ m}} \][/tex]

When we divide these values, we get:

[tex]\[ f = 4.2857142857142856 \times 10^{14} \text{ Hz} \][/tex]

To select the correct answer from our options, let's compare our result with the given choices:

A. [tex]\( 2.5 \times 10^{-14} \)[/tex] Hz
B. [tex]\( 4.3 \times 10^{14} \)[/tex] Hz
C. [tex]\( 1.7 \times 10^{-14} \)[/tex] Hz
D. [tex]\( 5.1 \times 10^{-14} \)[/tex] Hz

The result [tex]\( 4.2857142857142856 \times 10^{14} Hz \)[/tex] is very close to [tex]\( 4.3 \times 10^{14} Hz \)[/tex], which corresponds to option B.

Therefore, the correct answer is:

B. [tex]\( 4.3 \times 10^{14} \)[/tex] hertz