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3 years ago

10

A certain fm radio station broadcasts electromagnetic waves at a frequency of 125000 hertz. these radio waves travel at a speed

of 300,000,000 m/s what is the wavelength of these radio waves?

1 answer:

faltersainse [42]3 years ago

4 0

Speed = frequency x wavelength
300,000,000 = 125000 x wavelength
wavelength = 125000/300,000,000 =4.16667x10^-4 meters
or 4.1667E-4 meters

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$v_m=A\omega\\\Rightarrow v_m=A\sqrt{\dfrac{k}{m}}\\\Rightarrow v_m=6.25\times 10^{-2}\times \sqrt{\dfrac{74.5}{0.225}}\\\Rightarrow v_m=1.137278672\ m/s$

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Velocity is at any instant is given by

$\dfrac{v_m}{3}=\omega\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A\omega}{3}=\omega\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A}{3}=\sqrt{A^2-x^2}\\\Rightarrow \dfrac{A^2}{9}=A^2-x^2\\\Rightarrow A^2-\dfrac{A^2}{9}=x^2\\\Rightarrow x^2=\dfrac{8}{9}A^2\\\Rightarrow x=A\sqrt{\dfrac{8}{9}}\\\Rightarrow x=6.25\times 10^{-2}\sqrt{\dfrac{8}{9}}\\\Rightarrow x=\pm 0.0589255650989\ m$

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