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  = Î»₁  = 1500 m = 1.5 ï½˜ 10³ m

Frequency of 1st signal = f₁ = 200 kHz = 2 ｘ 10² ï½˜ 10³ Hz = 2 ｘ 10⁵ Hz

Frequency of the 2nd signal = f₂ = 1000 kHz = 1 ｘ 10³ ï½˜ 10³ Hz = 1ｘ 10⁶ Hz



To Find:


Wavelength of the 2nd signal = Î»₂ = ?

Speed of the electromagnetic radiation = v = ?

Solution:

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

v = f λ    or     Î» = `\frac{v}{f}`     or     f = `\frac{v}{λ}`


So to find Wavelength of 2nd signal Î»₂ 

λ₂ = `\frac{c}{f₂}`         [ v = c ]

by putting values

λ₂ = `\frac {3 ｘ 10⁸ m s⁻¹}{1 ｘ 10⁶ Hz}`

λ₂  = 3 ｘ 10² m 

or 

λ₂  = 300 m --------------Ans.


Speed of the electromagnetic radiation = v = ?


v = f₁ Î»₁       

by putting values

v =2 ｘ 10⁵ Hz ï½˜ 1.5 ï½˜ 10³ m

v =  3  ï½˜ 10⁸ m s⁻¹ --------------Ans.

By using the relation v = f₂ Î»₂ . Same answer can be obtained.


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