A transverse wave on a string is described by the equation y = (0.10 m) sin (2pi

ID: 2256453 • Letter: A

Question

A transverse wave on a string is described by the equation

y = (0.10 m) sin (2pi(x/4-2/t))

1. [3 points] Does a crest of the wave travel towards increasing x or decreasing x?

2. [5 points] What is the wavelength of the wave?

3. [5 points] What is the period of the wave?

4. [6 points] How far does a crest move in 5.0 s?

5. [6 points] What is the (sign and magnitude of the) transverse velocity of a bit of

string at the position x = 4.0 m at time t = 2.0 s?

Please help me the answers (1) increasing(2)4m(3)2s(4)10m(5)-0.31m/s

show work

y = (0.10 m) sin (2pi(x/4-2/t))

1) towards +ve x axis

2) here 2 pi/4 = coefficient of x= 2 pi/lamda ,

so lamda=4 m

3)2 pi/2 = coefficient of t= 2 pi/T , so T=2 sec

velocity of wave is given by c=frequency*wavelenght=2 m/s = lamda*(1/T)=4/2=2m/s

soin 5 sec distance is 2*5=10 m

5)diffrentiate y = (0.10 m) sin (2pi(x/4-t/2)) wrt t

v=-2*pi*0.05*cos(2pi(x/4-t/2))

at x=4m, t=2 sec

-2*pi*0.05*cos(2pi(4/4-2/2))=-0.314 m/s

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