Answer:
D) 31 m, 19 Hz
Explanation:
The equation of the wave in the problem is
[tex]y = 0.5 sin (0.20 x+120t)[/tex]
In general, the equation of a travelling wave is written as
[tex]y=Asin(kx+\omega t)[/tex]
where
A is the amplitude
[tex]k=\frac{2\pi}{\lambda}[/tex] is the wave number, with [tex]\lambda[/tex] being the wavelength of the wave
[tex]\omega=2\pi f[/tex] is the angular frequency and f is the frequency
By comparing the two equations, we see that for this wave:
[tex]k = 0.20 m^{-1}\\\omega = 120 rad/s[/tex]
So now we can use the two equations for k and [tex]\omega[/tex] to find the wavelength and the frequency of the wave:
[tex]\lambda=\frac{2\pi}{k}=\frac{2\pi}{0.20}=31 m\\f = \frac{\omega}{2\pi}=\frac{120}{2\pi}=19 Hz[/tex]
