It describes the wavelength-frequency relationship of an electromagnetic wave.

1. WAVELENGTH & FREQUENCY RELATIONSHIP
BY
JAYAM CHEMISTRY LEARNERS

2. Wavelength of an electromagnetic wave
1. It is the distance between the identical points on adjoining waveforms.
2. We measure it differently for transverse and longitudinal waves.
3. The length between the two adjacent crests or troughs is wavelength in transverse waves.
And in longitudinal waves, it is the calculation of the gap between the corresponding
compressions or rarefactions.
4. The Greek letter Lambda (λ) designates it.
5. The nanometer is the most commonly used unit to express the wavelength of
electromagnetic waves.
6. The instrument called "Wave meter" measures the wavelength of light radiations.

3. Frequency of an electromagnetic wave
1. The frequency is the number of waves that pass through a
given point in a unit time.
2. The symbol γ denotes it. Its units are cycles per second or
Hertz.
3. According to quantum theory, the energy of the photon
varies directly with the frequency.
4. Hence, with an increase in frequency, the energy of the
light radiation increases. And the less energetic light
radiations have lower frequencies.
Energy-Frequency
relationship

4. Relationship between the wavelength and frequency of an
electromagnetic wave:
According to quantum theory, the product of wavelength and frequency is equal to the velocity
of electromagnetic radiation in a vacuum.
Velocity= wavelength X frequency
Where,
c= velocity of light radiation in vacuum and its value is
3X108 m/sec
λ= wavelength of the light
γ= frequency of the light radiation

5. Why do shorter waves have higher frequencies
1. The wavelength of electromagnetic radiation
varies inversely with its frequency.
2. Hence, the shorter waves have higher
frequencies and vice versa.
3. When the wavelengths of the light radiations
decrease, their frequencies increase.
4. So, gamma rays have high frequencies and
shorter wavelengths in the electromagnetic
spectrum.

6. Numerical problem-1
Question: What happens to the wavelength of light when the frequency doubles?
Answer: The frequency and wavelength of light radiations are inversely proportional to each
other.
The inversely proportional relationship between the two is below:
Where,
λ= wavelength of the light
γ = frequency
c = velocity of the light in vacuum and is a constant quantity

7. Let us rewrite the above equation in terms of wavelength as below;
According to the question, when the frequency of a wave doubles, the modified wavelength
equation can be as below;

8. By comparing the above two equations, we will get as shown below;
It implies that when the frequency of a wave doubles, then its wavelength is reduced to
one-half.
Numerical problem-2
Question: How does the frequency of electromagnetic wave A compare to the frequency of
that of electromagnetic wave B if the ratio of their wavelengths is 1:3?

9. Let us consider the wavelength of electromagnetic wave A=x
The wavelength of electromagnetic wave B= 3x
We know that, the frequency and wavelength of the electromagnetic radiations are inversely
proportional to each other.
The inversely proportional relationship between the two is below:
The frequency of the electromagnetic wave A after putting the wavelength value is;

10. The frequency of the electromagnetic wave B after putting the wavelength value is;
By comparing the frequencies of both the electromagnetic waves A & B we get;

11. Hence, the ratio of frequencies of electromagnetic waves A & B is 3:1.
Numerical problem-3
A transmitter emits electromagnetic radiation having a frequency of 1.368 kHz. Calculate
its wavelength?
The formula to calculate the wavelength of electromagnetic radiation is;
Where,
γ = frequency
c= velocity of the light in vacuum and is a constant quantity

12. Substituting the values of c and γ in the above equation, we get;
λ =
3 × 108 𝑚/𝑠
1.368 × 103𝑠−1
1 kHz= 103 HZ = 103 s-1
λ= 2.1929X105 m

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