Respuesta :
Answer:
[tex] v = \lambda f[/tex] (1)
And we have this other relationship between the linear speed and the angular speed:
[tex] v = rw[/tex] (2)
We can find the linear velocity like this:
[tex] v = 0.08 m * 3.49 \frac{rad}{s}= 0.279 m/s[/tex]
And then from equation (1) we can solve for the frequency and we got:
[tex] \lambda = \frac{v}{f}[/tex]
And replacing we got:
[tex]\lambda = \frac{0.279 m/s}{4000 Hz}= 6.98x10^{-5} m[/tex]
And that represent the wavelength in th groove for this case.
Explanation:
For this case we have the following data given:
[tex] w = 3.49 rad/s[/tex] represent the angular velocity
[tex] f = 4 kHz *\frac{1000 Hz}{1 kHz}= 4000 Hz[/tex] represent the frequency
[tex] r = 0.08 m[/tex] we assume that this respresent the distance from the center
We know the following relationship between the wavelength [tex]\lambda[/tex] and the velocity of a wave:
[tex] v = \lambda f[/tex] (1)
And we have this other relationship between the linear speed and the angular speed:
[tex] v = rw[/tex] (2)
We can find the linear velocity like this:
[tex] v = 0.08 m * 3.49 \frac{rad}{s}= 0.279 m/s[/tex]
And then from equation (1) we can solve for the frequency and we got:
[tex] \lambda = \frac{v}{f}[/tex]
And replacing we got:
[tex]\lambda = \frac{0.279 m/s}{4000 Hz}= 6.98x10^{-5} m[/tex]
And that represent the wavelength in th groove for this case.
