Question

What is the frequency of a yellow lamp with a wavelength of 590 nm?

Answer 1

Hint: To solve this question we first need to know what is wavelength. Wavelength is the distance between two successive troughs of a wave, or the distance between two successive crests of a wave.

Complete answer:
We know that frequency is defined as the number of vibrations or cycles per unit of time. It is denoted either by the Greek letter $\nu $ or by \[\].
Now, in wave propagation, the relation between wavelength and frequency, in a vacuum, can be given by
\[\nu =\dfrac{c}{\lambda }\]
Where $\nu $ is the frequency, $\lambda $ is the wavelength and c is the speed of light (3$\times {{10}^{8}}$ m/s).
From this equation, we can see that frequency and wavelength are inversely proportional. That means that when there is an increase in wavelength, the frequency decreases.
The SI unit of speed is m/s and the SI unit of wavelength is m. So, the SI suit of frequency ${{s}^{-1}}$ is Hertz and has the dimensions ${{T}^{-1}}$.
Now, a yellow lamp produces light of the wavelength 590 nm.
We know that 1 nanometer or 1 nm = 1$\times {{10}^{-9}}$ m.
So, the wavelength of light produced by a yellow lamp is 590$\times {{10}^{-9}}$ m.
Hence,
\[\begin{align}
  & \nu =\dfrac{3\times {{10}^{8}}}{590\times {{10}^{-9}}} \\
 & \nu =5.085\times {{10}^{14}}{{s}^{-1}} \\
\end{align}\]
The frequency of light produced from a yellow lamp with a wavelength of 590 nm is \[5.085\times {{10}^{14}}{{s}^{-1}}\].

Note:
Frequency can also be defined from the equation that defines the relationship between time period and frequency.
\[=\dfrac{1}{T}\]
Where time period (T) can be defined as the time taken to complete one cycle of a repeated occurrence.