Chapter 5, Problem 13STP

Interpretation Introduction

Interpretation: The drawing showing the electromagnetic wave with the lowest frequency needs to be identified.

Concept Introduction: When an electric field and a magnetic field are coupled together, an electromagnetic wave is formed. Here, electric and magnetic fields are perpendicular to each other as well as the direction of the wave.

Here, the wavelength of a wave is defined as the distance between two successive crests and troughs. The frequency of a wave is the number of waves passing a point in one second. The amplitude of a wave is determined by the height of the crests and troughs formed in the electromagnetic waves.

Moreover, the energy of the wave is inversely proportional to its wavelength. This can be explained by the following formula:

  $E=\frac{hc}{\lambda }$

Here, h is Planck’s constant and c is the speed of light. Both are constant; thus, the above relation can be rewritten as follows:

  $E\propto \frac{1}{\lambda }$

Here, E is energy and $\lambda$ is the wavelength of light.

Answer to Problem 13STP

Correct answer is option (A).

Explanation of Solution

Reason for correct option:

The frequency of a wave is the number of waves passing a point in one second. If there are a smaller number of crests and troughs in a wave per second, the frequency of the wave will be low.

Also, the wave with the longest wavelength will have the largest distance between two successive crests and the trough of the wave.

The wave with the largest distance is shown below:

  

Since wavelength is inversely proportional to wavelength $\left(v=\frac{c}{\lambda }\right)$ , thus, it will have the lowest frequency.

Thus, the correct option is (A).

Conclusion

Reason for incorrect options:

From the given drawings, drawing in option (A) has a wave with the longest wavelength because there the distance between two successive crests and trough is large.

The other waves are as follows:

  

  

Here, the distance between two successive crests and trough is small as compared to the one given in option (A). Thus, these waves’ frequencies will be comparatively higher.

Moreover, the number of crests and troughs forming per second is more in the above waves; thus, they have a higher frequency.

Thus, options (B) and (C) are incorrect.