Answer:
Explanation:
A general wave function is given by:
[tex]f(x,t)=Acos(kx-\omega t)[/tex]
A: amplitude of the wave = 0.075m
k: wave number
w: angular frequency
a) You use the following expressions for the calculation of k, w, T and λ:
[tex]\omega = 2\pi f=2\pi (2.00Hz)=12.56\frac{rad}{s}[/tex]
[tex]k=\frac{\omega}{v}=\frac{12.56\frac{rad}{s}}{12.0\frac{m}{s}}=1.047\ m^{-1}[/tex]
[tex]T=\frac{1}{f}=\frac{1}{2.00Hz}=0.5s\\\\\lambda=\frac{2\pi}{k}=\frac{2\pi}{1.047m^{-1}}=6m[/tex]
b) Hence, the wave function is:
[tex]f(x,t)=0.075m\ cos((1.047m^{-1})x-(12.56\frac{rad}{s})t)[/tex]
c) for x=3m you have:
[tex]f(3,t)=0.075cos(1.047*3-12.56t)[/tex]
d) the speed of the medium:
[tex]\frac{df}{dt}=\omega Acos(kx-\omega t)\\\\\frac{df}{dt}=(12.56)(1.047)cos(1.047x-12.56t)[/tex]
you can see the velocity of the medium for example for x = 0:
[tex]v=\frac{df}{dt}=13.15cos(12.56t)[/tex]
