Question

1-

A wave travels along a string in the positive x -direction at 23.8 m/s . The frequency of the wave is 51.3 Hz . At x = 0 and t = 0 , the velocity of the string in the y -direction is 2.11 m/s and the vertical displacement is y = 2.31 mm . Write the function y(x, t) for the wave. Pont A in the figure below is 39.1 cm below the ceiling. Determine how much longer it will take for a wave pulse to travel from point A to the ceiling along wire 1 than along wire 2.

2-

Answer 1

Wavelength=speed/f=23.8/51.3=0.464m

y(0,0)=0.00231=ASin(phi)

dy/dt at(0,0)=2.11=-A*2pi*f*Cos(phi)=-A*51.3*2pi*Cos(phi)

A=-0.00655m=-6.55mm, phi=0.00231 rad

k=2pi/lamda=2pi/0.464=13.54 m^-1

2pi*f*t=__*pi*t

Third blank is 2f=102.6

y=-6.55mmSin(13.54m^-1 x-102.6 pi t+0.00231)

2)T1Cos60+T2Cos30=mg

T1Sin60=T2Sin30

T1=mg/2

T2=sqrt(3)mg/2

t1=l1/sqrt(T1/u)=(0.391/Cos(60))/sqrt(mg/2u)

t2=l2/sqrt(T2/u)=(0.391/Cos(30))/(sqrt(sqrt(3)mg/2u)

t1/t2=(Cos (30)/Cos(60))*(sqrt(sqrt(3))=2.28

t1=2.28t2

Answer 2

Wavelength=speed/f=23.8/51.3=0.464m

y(0,0)=0.00231=ASin(phi)

dy/dt at(0,0)=2.11=-A*2pi*f*Cos(phi)=-A*51.3*2pi*Cos(phi)

A=6.94mm and phi=2.80 radians

k=2pi/lamda=2pi/0.464=13.54 m^-1

2pi*f*t=__*pi*t

Third blank is 2f=102.6

y=6.94mmSin(13.54m^-1 x-102.6 pi t+2.80)

2)T1Cos60+T2Cos30=mg

T1Sin60=T2Sin30

T1=mg/2

T2=sqrt(3)mg/2

t1=l1/sqrt(T1/u)=(0.391/Cos(60))/sqrt(mg/2u)

t2=l2/sqrt(T2/u)=(0.391/Cos(30))/(sqrt(sqrt(3)mg/2u)

t1/t2=(Cos (30)/Cos(60))*(sqrt(sqrt(3))=2.28

t1=2.28t2

Answer 3