## anonymous one year ago 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

1. Michele_Laino

we can write these equations: for waves A and B: $\Large \begin{gathered} {\lambda _A}{f_A} = {v_A} \hfill \\ \hfill \\ {\lambda _B}{f_B} = {v_B} \hfill \\ \end{gathered}$

2. Michele_Laino

f is the frequency

3. Michele_Laino

now, we have: f_A=2*f_B, and v_A=v_B, so we can write:

4. anonymous

ok:)

5. Michele_Laino

step, by step: $\Large \begin{gathered} {\lambda _A}{f_A} = {\lambda _B}{f_B} \hfill \\ {\lambda _A}\left( {2{f_B}} \right) = {\lambda _B}{f_B} \hfill \\ 2{\lambda _A}{f_B} = {\lambda _B}{f_B} \hfill \\ \hfill \\ 2{\lambda _A} = {\lambda _B} \hfill \\ \end{gathered}$

6. 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?

7. Michele_Laino

no, the wavelwngth of B is twice of the wave length of A

8. Michele_Laino

wavelength*

9. anonymous

ohh okay! so that means the answer should be choice C ?

10. Michele_Laino

namely the wavelength of B is greater than the wavelength of A

11. Michele_Laino

yes! that's right!

12. anonymous

ahh okie! yay! thank you:)

13. Michele_Laino

thank you! :)