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.

a electromagnetic waves

search it up!

explanation: