At what velocity would a spacecraft have to be moving for a radio station on earth transmitting at 102 mhz to be picked up by a radio tuned to 101.6 mhz ?

Respuesta :

Answer;

v = 1.165 × 10^6 m/s

Explanation;

Δf = –v/λ = –vf/s  

v = velocity of source relative to listener  

λ = wavelength of source, relative to source  

f = frequency of source, relative to source  

s = speed of wave in medium

C = speed of light = 3 × 10^8 m/s

Δf = vf/s

   = 102 - 101.6 = 0.4 MHz = 400 kHz

v = 400 kHz x 3 ×10^8 / 103 000 kHz  

v = 1.165 × 10^6 m/s

The velocity of spacecraft will be "1.165 × 10⁶ m/s".

Wavelength and Frequency:

According to the question,

Speed of light, C = 3×10⁸ m/s

Frequency, 102 mhz

                    101.6 mhz

As we know the relation,

→ [tex]\Delta f = -\frac{v}{\lambda}[/tex]

        [tex]= -\frac{vf}{s}[/tex]

then,

→ v = 102 - 101.6  

     = 0.4 MHz or, 400 kHz

hence,

The velocity will be:

→ v = [tex]400\times \frac{3\times 10^{-8}}{103000}[/tex]

     = [tex]1.165\times 10^{6}[/tex] m/s

Thus the above response is appropriate.

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