A string with linear density 2.0 g/m is stretched along the positive x -axis wit

Question

A string with linear density 2.0 g/m is stretched along the positive x-axis with tension 20 N. One end of the string, at x=0m, is tied to a hook that oscillates up and down at a frequency of 100 Hz with a maximum displacement of 1.0 mm. At t=0s, the hook is at its lowest point.

velocity=100 m/s , wavelength=1 m , Amplitude= 1 mm

a) What is the phase constant of the wave?

I know that the answer is -1.57, so why isn't it +1.57?

b) Find the equation for the displacement D(x,t) of the traveling wave.

I know that the answer is D(x,t)=(1.0mm)sin[(2rad/m)x (200rad/s)t 2)], but I wanna know what makes its angular velocity -200 instead of +200 ??

Thanks in advance.

Explanation / Answer

a) The equation of the displacement of the wave is:

D(x,t)=Asin[kx +/wt +]

for t =0 we have:

D(x,0)=Asin[kx +0+]

the position of the hook (x =0) is at its lowest point, this is x0=-A

D(0,0)=-A=Asin[0 +0+]

so sin[]=-1

so = -/2 = -1.57 rad

B) the sign in the equation give as the direction of the velocity, the wave is traveling to the right so it must be negative

D(x,t)=Asin[kx wt +]

If you a positive value for wt the wave travels to the left, this is no the case.

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