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I don't know how to solve question like this:

A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by:y = 0.006 cos π(46t - 12x). The frequency of the wave, in SI units, is closest to ...

Will appreciate your help!

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Hint: Frequency has dimension of inverse time and the argument for cos must be a pure number. – Alfred Centauri Jul 5 '12 at 14:55
up vote 1 down vote accepted

This sounds suspiciously like a homework problem, which means we are only allowed to discuss general concepts. Your professor wouldn't be best pleased if we just gave you the answer to their problems :-)

The amplitude $y$ is a function of time and distance. Since you just want the frequency the $x$ dependance doesn't matter and you can just look at the amplitude at a fixed value of $x$. I would choose $x = 0$ as the simplest option.

Now you have the amplitude as a function of just time. You have to work out how long it takes for the amplitude to go through one cycle. For example suppose you start at $t = 0$, then as you increase $t$ the value $y(t)$ will fall to zero, go negative, start rising again and eventually return to it's original value. That time is the period. Once you know the period the frequency is just the reciprocal of the period.

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