Radio Waves Formula

Radio waves are defined as waves with a large wavelength that can propagate along the curvature of the earth. They are a part of the spectrum with frequencies lower than visible light, rendering them undetectable to the naked eye. Radio waves propagate in different ways depending on their frequency. These are wide spectrum waves that may be sent and received by transmitters and receivers.  The frequency changes depending on how they interact with different environments, particularly whether they penetrate materials and how they interact with the Earth’s ionosphere. They are also known as ground or surface waves. They operate at frequencies ranging from 300 GHz to 3 kHz.

What are Radio Waves?

The concept of radio waves is explained by their speed formula. The speed of a radio wave is calculated by computing the product of its wavelength and frequency. 

• It is denoted by the symbol v_r. 
• Its standard unit of measurement is meters per second (m/s). 
• And the dimensional formula is given by [M⁰L¹T^-1].

Radio Waves Formula

The formula to calculate the radio waves is given by,

v_r = λv

where,

• v_r is the speed,
• λ is the wavelength, and
• v is the frequency of the radio wave.

Sample Problems

Problem 1: Calculate the speed of a radio wave having a wavelength of 280 m and a frequency of 1 MHz. 

Solution:

We have,

λ = 280

v = 1 × 10⁶

Using the formula we have,

v_r = λv

= 280 (10⁶)

= 2.8 × 10⁷ m/s

Problem 2: Calculate the speed of a radio wave having a wavelength of 35 m and a frequency of 2 MHz.

Solution:

We have,

λ = 35

v = 2 × 10⁶

Using the formula we have,

v_r = λv

= 35 (2 × 10⁶)

= 7 × 10⁷ m/s

Problem 3: Calculate the speed of a radio wave having a wavelength of 150 m and a frequency of 1.5 kHz.

Solution:

We have,

λ = 150

v = 1.5 × 10³

Using the formula we have,

v_r = λv

= 150 (1.5 × 10³)

= 2.25 × 10⁵ m/s

Problem 4: Calculate the wavelength of a radio wave having a speed of 3 × 10⁶ m/s and a frequency of 1.5 MHz.

Solution:

We have,

v_r = 3 × 10⁶

v = 1.5 × 10⁶

Using the formula we have,

v_r = λv

λ = (3 × 10⁶)/(1.5 × 10⁶)

= 2 m

Problem 5: Calculate the wavelength of a radio wave having a speed of 4 × 10⁶ m/s and a frequency of 2 kHz.

Solution:

We have,

λ = 4 × 10⁶

v = 2 × 10³

Using the formula we have,

v_r = λv

λ = (4 × 10⁶)/(2 × 10³)

= 2000 m

Problem 6: Calculate the frequency of a radio wave having a speed of 5 × 10⁶ m/s and a wavelength of 500 m.

Solution:

We have,

v_r = 5 × 10⁶

λ = 500

Using the formula we have,

v_r = λv

v = (5 × 10⁶)/500

= 10 kHz

Problem 7: Calculate the frequency of a radio wave having a speed of 2.5 × 10⁷ m/s and a wavelength of 800 m.

Solution:

We have,

v_r = 2.5 × 10⁷

λ = 800

Using the formula we have,

v_r = λv

v = (2.5 × 10⁷)/800

= 31.2 kHz

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