anonymous
  • anonymous
Consider two waves traveling at the same velocity. Wave A has twice the frequency of Wave B. Which of the following statements is true? A. The wavelengths of both waves are equal. B. The wavelength of Wave A is greater than that of Wave B. C. The wavelength of Wave B is greater than that of Wave A. D. The wavelength of the waves has no relevance to the speed. **Thank you! :D
Physics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Michele_Laino
  • Michele_Laino
we can write these equations: for waves A and B: \[\Large \begin{gathered} {\lambda _A}{f_A} = {v_A} \hfill \\ \hfill \\ {\lambda _B}{f_B} = {v_B} \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
f is the frequency
Michele_Laino
  • Michele_Laino
now, we have: f_A=2*f_B, and v_A=v_B, so we can write:

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anonymous
  • anonymous
ok:)
Michele_Laino
  • Michele_Laino
step, by step: \[\Large \begin{gathered} {\lambda _A}{f_A} = {\lambda _B}{f_B} \hfill \\ {\lambda _A}\left( {2{f_B}} \right) = {\lambda _B}{f_B} \hfill \\ 2{\lambda _A}{f_B} = {\lambda _B}{f_B} \hfill \\ \hfill \\ 2{\lambda _A} = {\lambda _B} \hfill \\ \end{gathered} \]
anonymous
  • anonymous
okay! and so does that mean the wavelength of A is greater than the wavelength of B? so choice B would be the solution?
Michele_Laino
  • Michele_Laino
no, the wavelwngth of B is twice of the wave length of A
Michele_Laino
  • Michele_Laino
wavelength*
anonymous
  • anonymous
ohh okay! so that means the answer should be choice C ?
Michele_Laino
  • Michele_Laino
namely the wavelength of B is greater than the wavelength of A
Michele_Laino
  • Michele_Laino
yes! that's right!
anonymous
  • anonymous
ahh okie! yay! thank you:)
Michele_Laino
  • Michele_Laino
thank you! :)

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