What are the wavelengths of a television station which transmits vision or 500 MHz and sound at 505 MHz respectively? Take the speed of electromagnetic waves as 3 ｘ 10⁸ m s⁻¹. (60.0 cm, 59.4 cm.) 


Given:

Frequency of vision transmission = f₁ = 500 MHz = 5 ｘ 10² ï½˜ 10⁶ Hz = 5.0 ｘ 10⁸ Hz
Frequency of sound transmission = f₂ = 505 MHz = 5.05 ｘ 10² ï½˜ 10⁶ Hz = 5.05 ｘ 10⁸ Hz
Speed of the electromagnetic radiation = v = 3  ï½˜ 10⁸ m s⁻¹

To Find:

The wavelength of vision transmission = λ₁ =?
The wavelength of sound transmission = Î»₂ = ?

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 the Wavelength of vision transmission λ₁ 

λ₁ = `\frac{c}{f₁}`         [ v = c ]

by putting values

λ₁ = `\frac{3 ｘ 10⁸ m s⁻¹}{5.05 ｘ 10⁸ Hz}`

λ₁ = 0.594 m

or 

λ₁ = 59.4 cm --------------Ans.


The wavelength of sound transmission = Î»₂

λ₂ = `\frac{c}{f₂}`     [ v = c ]

by putting values

λ₂ = `\frac{3  ï½˜ 10⁸ m s⁻¹}{5.0 ｘ 10⁸ Hz}`

λ₂ = 0.6 m

or 

λ₁ = 60 cm --------------Ans.




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