Question

Calculate the frequency, phase velocity and maximum particle velocity for y=0.2sin (0.8x-40t)

Answer 1

(a)

$$\omega=2\pi f,$$ $$f=\dfrac{\omega}{2\pi}=\dfrac{40\ \dfrac{rad}{s}}{2\pi}=6.37\ Hz.$$

(b)

$$v_{p} = \dfrac{\omega}{k}=\dfrac{40\ \dfrac{rad}{s}}{0.8\ m^{-1}}=50\ \dfrac{m}{s}.$$

(c) The particle velocity can be found as follows:

$$v=\dfrac{dy}{dt}=-8cos(0.8x-40t).$$

The maximum particle velocity will be when $cos(0.8x-40t)=\pm1$. Therefore, the magnitude of the maximum particle velocity equals $v_{max}=8\ m/s.$

Answer:

(a) $f=6.37\ Hz.$

(b) $v_{p} =50\ \dfrac{m}{s}.$

(c) $v_{max}=8\ m/s.$