A 3.49 rad/s (33 1/3 rpm) record has a 4.00 kHz tone cut in the groove. If the groove is located d = 0.080 m from the center of the record (see drawing), what is the wavelength in the groove?

  (1)

And we have this other relationship between the linear speed and the angular speed:

 (2)

We can find the linear velocity like this:

And then from equation (1) we can solve for the frequency and we got:

And replacing we got:

And that represent the wavelength in th groove for this case.

Explanation:

For this case we have the following data given:

represent the angular velocity

represent the frequency

we assume that this respresent the distance from the center

We know the following relationship between the wavelength and the velocity of a wave:

  (1)

And we have this other relationship between the linear speed and the angular speed:

 (2)

We can find the linear velocity like this:

And then from equation (1) we can solve for the frequency and we got:

And replacing we got:

And that represent the wavelength in th groove for this case.

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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