The wavelength of the signals from a radio transmitter is 1500 m and the frequency is 200 Khz. What is the wavelength for a transmitter operating at 1000 Khz and with what speed the radio waves travel. (Ans: 300 m, 3 x10⁸ m s⁻¹)



Data Given:


Wavelength of the 1st signal  = λ₁  = 1500 m = 1.5 x 10³ m

Frequency of 1st signal = f₁ = 200 kHz = 2 x 10² x 10³ Hz = 2 x 10⁵ Hz

Frequency of the 2nd signal = f = 1000 kHz = 1 x 10³ x 10³ Hz = 1x 10⁶ Hz



To Find:


Wavelength of the 2nd signal = λ₂ = ?

Speed of the electromagnetic radiation = v = ?

Solution:

The general relation among wavelength (λ), speed (v), and frequency (f) is following:

v = f λ    or     λ = vf     or     f = vλ


So to find Wavelength of 2nd signal λ₂ 

λ₂ = cf         [ v = c ]

by putting values

λ₂ = 310ms¹110 Hz

λ₂  = 3 x 10² m 

or 

λ₂  = 300 m --------------Ans.


Speed of the electromagnetic radiation = v = ?


v = f λ       

by putting values

v =2 x 10⁵ Hz  1.5 x 10³ m

 3  x 10⁸ m s⁻¹ --------------Ans.

By using the relation v = f₂ λ . Same answer can be obtained.


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