Question

If c is the speed, \[\nu \] is the frequency and \[\lambda \] is wavelength of EM waves, then
A. \[c = \nu \lambda \]
B. \[\dfrac{\lambda }{\nu } = c\]
C. \[\dfrac{\nu }{\lambda } = c\]
D. \[\dfrac{1}{\lambda } = \dfrac{c}{\nu }\]

Answer 1

Hint: We will use the basic concept of speed of an EM wave, expressed as the ratio of distance and time period of that wave. The relationship between frequency and time period of the given wave will be used to deduce the final answer.

Complete step by step answer:
The speed of an electromagnetic wave is the distance traveled by the wave in one second.
\[c = \dfrac{{{\text{distance travelled in one second}}}}{{{\text{time period}}}}\]

Wavelength is the length of one complete cycle of the given electromagnetic wave. In other words, we can say that wavelength is equal to the distance covered by the wave in one cycle.

Substitute \[\lambda \] for distance traveled in one second in the above equation.
\[c = \dfrac{\lambda }{{{\text{time period}}}}\]……(1)

An electromagnetic wave frequency is equal to the total number of cycles completed by that wave in one second. We also know that the frequency of a wave is equal to the inverse of its time period.
\[\begin{array}{l}
\nu = \dfrac{1}{T}\\
T = \dfrac{1}{\nu }
\end{array}\]
Here T is the time period.

Substitute \[\dfrac{1}{\nu }\] for the time period in equation (1).
\[\begin{array}{l}
c = \dfrac{\lambda }{{\left( {\dfrac{1}{\nu }} \right)}}\\
c = \nu \lambda
\end{array}\]

Therefore, we can say that the speed of the given EM wave is equal to the product of its frequency and time period

So, the correct answer is “Option A”.

Note:
We have to remember that the frequency of a wave is inverse of its time period.
Additional information: When a white beam of light is allowed to pass through a prism, it will separate into a pattern of seven different colors, which has different wavelengths and frequencies. This pattern obtained is called the electromagnetic spectrum, and the waves obtained are electromagnetic waves