The Vividh Bharati Station of All India Radio, Delhi broadcasts on a frequency of \(1368 \mathrm{kHz}\) (kilo hertz). Calculate the wavelength and wave number of the electromagnetic radiation emitted by the transmitter. Which part of the electromagnetic spectrum does it belong to?

Understanding the relationship between frequency and wavelength is fundamental in the study of electromagnetic radiation. When a radio station, like the Vividh Bharati Station of All India Radio, broadcasts at a certain frequency, the wavelength of the electromagnetic waves can be calculated using the speed of light.

The speed of light, denoted as 'c', is a constant approximately equal to \(3.00 \times 10^8 \text{ m/s}\) in a vacuum. The frequency, denoted as 'f', is the number of oscillations per second and is given in hertz (Hz). In our example, the frequency is provided as \(1368 \text{ kHz}\) or \(1368 \times 10^3 \text{ Hz}\).

The formula to convert frequency to wavelength is expressed as \( \text{Wavelength (λ) } = \frac{\text{Speed of light (c)}}{\text{Frequency (f)}} \). Using this formula, when the frequency is converted to hertz and applied, it results in the wavelength of the emitted radio waves.

It is essential to remember not to confuse kilohertz with hertz, as their mismatch can lead to incorrect calculations. Multiplying kilohertz by 1,000 converts it to hertz, aligning the units for the formula and ensuring an accurate wavelength calculation.

After determining the wavelength, the next step is to calculate the wavenumber. A wavenumber gives you a measure of how many wavelengths fit into a meter and is particularly useful in fields like spectroscopy.

The wavenumber, denoted as 'k', is inversely related to the wavelength and is calculated using the formula \( \text{Wavenumber (k) } = \frac{1}{\text{Wavelength (λ)}} \). It is expressed in units of inverse meters \( m^{-1} \).

This concept may sometimes seem abstract, but a handy analogy would be to think of it as the number of wave peaks that pass a certain point over a set distance, similar to counting the number of fence posts over a specific length of fence.

Higher wavenumbers correspond to shorter wavelengths and typically higher energy states, while lower wavenumbers indicate longer wavelengths and lower energy states.

The electromagnetic spectrum encompasses all possible wavelengths of electromagnetic radiation, from very short gamma rays to very long radio waves. The radio spectrum is part of this larger electromagnetic spectrum and is classified into different bands based on the frequency and wavelength of the radio waves.

For example, in the case of the Vividh Bharati Station broadcasting at \(1368 \text{ kHz}\), the waves fall within the Medium Frequency (MF) range. This range is known for its ability to be reflected by the Earth's ionosphere and is commonly used for AM broadcasting.

The radio spectrum is generally divided into these bands:

Microwave Frequency (MF)

• Extremely High Frequency (EHF)
• Super High Frequency (SHF)
• Ultra High Frequency (UHF)

Radio Frequency (RF)

• Very High Frequency (VHF)
• High Frequency (HF)
• Medium Frequency (MF)
• Low Frequency (LF)
• Very Low Frequency (VLF)

Classifying the frequency helps in determining the suitable applications for that particular wave, such as communication distances, broadcast types, and quality.