Answer to Question #241458 in Physics for Tammy

Question #241458
Calculate the frequency, phase velocity and maximum particle velocity for y=0.2sin (0.8x-40t)
1
Expert's answer
2021-09-24T09:25:56-0400

(a)

ω=2πf,\omega=2\pi f,f=ω2π=40 rads2π=6.37 Hz.f=\dfrac{\omega}{2\pi}=\dfrac{40\ \dfrac{rad}{s}}{2\pi}=6.37\ Hz.

(b)

vp=ωk=40 rads0.8 m1=50 ms.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=dydt=8cos(0.8x40t).v=\dfrac{dy}{dt}=-8cos(0.8x-40t).

The maximum particle velocity will be when cos(0.8x40t)=±1cos(0.8x-40t)=\pm1. Therefore, the magnitude of the maximum particle velocity equals vmax=8 m/s.v_{max}=8\ m/s.

Answer:

(a) f=6.37 Hz.f=6.37\ Hz.

(b) vp=50 ms.v_{p} =50\ \dfrac{m}{s}.

(c) vmax=8 m/s.v_{max}=8\ m/s.


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