The following can be arranged in decreasing order of wave number
A. AM radio
B. TV and FM radio
C. Microwave
D. Short radio wave

Options

A. ` A gt B gt D gt C`
B. ` C gt D gt B gt A`
C. `A gt B gt C gt D`
D. `D gt C gt B gt A`

Answer

To arrange the given electromagnetic waves in decreasing order of wave number, we need to understand the relationship between wave number (k) and wavelength (λ). The wave number is defined as:

\[ k = \frac{2\pi}{\lambda} \]

From this equation, we can see that wave number (k) is inversely proportional to wavelength (λ). This means that as the wavelength increases, the wave number decreases, and vice versa.

Now, let's analyze the given options:

1. **AM Radio Waves (A)**: These have the longest wavelength among the options, which means they will have the lowest wave number.
2. **TV and FM Radio Waves (B)**: These have shorter wavelengths than AM radio waves, so they will have a higher wave number than AM waves but lower than microwaves.
3. **Microwaves (C)**: Microwaves have shorter wavelengths than both AM and FM/TV radio waves, resulting in a higher wave number.
4. **Short Radio Waves (D)**: These have even shorter wavelengths than microwaves, giving them the highest wave number.

Now, we can arrange the waves in decreasing order of wave number:

1. **Microwaves (C)** - highest wave number
2. **Short Radio Waves (D)**
3. **TV and FM Radio Waves (B)**
4. **AM Radio Waves (A)** - lowest wave number

Thus, the final arrangement in decreasing order of wave number is:

**C > D > B > A**