In: Physics
A fellow student of mathematical bent tells you that the wave
function of a traveling wave on a thin rope is
y(x,t)= 2.10 mm cos[( 7.02 rad/m
)x+( 749 rad/s )t].Being more practical-minded,
you measure the rope to have a length of 1.34 m and a mass of 3.32
g .
Part A
Determine the amplitude.
Part B
Determine the frequency
Part C
Determine the wavelength.
Part D
Determine the wave speed.
Part E
Determine the direction the wave is traveling.
−x−direction | |
+x−direction |
Part F
Determine the tension in the rope.
Part G
Determine the average power transmitted by the wave.
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Given that
A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is
y(x,t)= 2.10 mm cos[( 7.02 rad/m )x+( 749 rad/s )t]
Mass of the rope (m) =3.32g =3.32*10-3kg
Length of the rope is (L) =1.34m
a)
We know that
y(x.t) =Acos(wt+kx)
Comparing with the given equation we get
Amplitude is (A) =2.10mm =0.0021m
b)
The frequency of the wave is given by
w =2pif
f =w/2pi from the above equation w =749rad/s
=749/6.28 =119.2675HZ
c)
The wavelength of the wave is given by
k =2pi/lamda
lamda =2pi/k = 6.28/7.02 = 0.8945m (k=7.02 rad/m from the above equation ))
d)
The speed of the wave is given by
v =f*lamda =(119.2675HZ)( 0.8945m )=106.695m/s
e)
The direction of the string will be in the negative x-direction(-x)
f)
The tension in the rope is
v =Sqrt(T/u)
v2 =T/u ===> T =v2*u =v2*(m/L) =(106.695m/s)2(3.32*10-3kg/1.34) =28.2047N
g)
The average power transmitted by the wave is
P =(1/2)uvw2A2 =0.5*(3.32*10-3kg/1.34)(106.695m/s)( 749 rad/s )2(0.0021m)2 =0.327W