Respuesta :
Answer
given,
y(x,t)= 2.20 mm cos[( 7.02 rad/m )x+( 743 rad/s )t]
length of the rope = 1.33 m
mass of the rope = 3.31 g
comparing the given equation from the general wave equation
y(x,t)= A cos[k x+ω t]
A is amplitude
now on comparing
a) Amplitude = 2.20 mm
b) frequency =
[tex]f = \dfrac{\omega}{2\pi}[/tex]
[tex]f = \dfrac{743}{2\pi}[/tex]
f = 118.25 Hz
c) wavelength
[tex]k= \dfrac{2\pi}{\lambda}[/tex]
[tex]\lambda= \dfrac{2\pi}{k}[/tex]
[tex]\lambda= \dfrac{2\pi}{7.02}[/tex]
[tex]\lambda= 0.895\ m[/tex]
d) speed
[tex]v = \dfrac{\omega}{k}[/tex]
[tex]v = \dfrac{743}{7.02}[/tex]
v = 105.84 m/s
e) direction of the motion will be in negative x-direction
f) tension
[tex]T = \dfrac{v^2\ m}{L}[/tex]
[tex]T = \dfrac{(105.84)^2\times 3.31 \times 10^{-3}}{1.33}[/tex]
T = 27.87 N
g) Power transmitted by the wave
[tex]P = \dfrac{1}{2}m\ v \omega^2\ A^2[/tex]
[tex]P = \dfrac{1}{2}\times 0.00331\times 105.84\times 743^2\ 0.0022^2[/tex]
P = 0.438 W
