A wave with frequency 10.2Hz and amplitude 42.2 mm moves in the positive x direction with a speed of 4.3 ms What is the waves angular frequency?

Answer 1

If the angular frequency is really what you want to know, then you don't need the amplitude
or speed. All you need is the frequency, and the angular frequency is just that times [ 2 pi ].

w ('omega', or angular frequency) = 10.2 x 2 pi = 64.0885 radians per second (rounded)

Sometimes this is hard to understand or explain. But it's clear if we use degrees instead of radians ...

If your 10.2 Hz means that you have a wheel turning 10.2 times a second, then how many degrees
does it turn in a second ?

Well, there are 360 degrees in one whole turn, so 10.2 turns is (360 x 10.2) = 3,672 degrees per second.

That's all there is to it. That's the 'angular' velocity. But it's normally done in radians instead of degrees,
and there are [ 2 pi ] radians in one whole turn.

Answer 2

To calculate the angular frequency (ω) of the wave, you can use the formula ω = 2πf, where f is the frequency of the wave. Given that the frequency is 10.2 Hz, the angular frequency would be 2π * 10.2 = 64.08 rad/s.