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I was wondering what the difference is between speed in the formula $v=fλ$ and maximum velocity in the formula $v=ωY_{\max}$ as applied to a wave.

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$v=f\lambda$ refers to the relationship between the speed of a wave that is travelling through a medium to its frequency and wavelength.

Now, forget the waves and come to oscillations for example like the simple pendulum.

The position of the Bob is $x=x_0 sin(\omega t+ \phi)$ . If you differentiate this with respect to time, we get

$\dot x = \omega x_0 cos( \omega t + \phi)$ This is the formula of the velocity of the bob whose amplitude is given by

$\dot x_{max} = v_{max}= \omega x_0$, which is what you wanted.

You got confused between waves and oscillations.

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  • $\begingroup$ Thanks for explaining, that's really helpful! $\endgroup$
    – uzzy
    May 30 at 10:45

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