1.) A wave on a string is described by D(x,t)=(2.8cm)× sin[2(x/(6.0m)+t/(0.16s)+

Question

1.) A wave on a string is described by D(x,t)=(2.8cm)× sin[2(x/(6.0m)+t/(0.16s)+1)], where x is in m and t is in s.

At t=0.32s, what is the displacement of the string at x=6.5m?

2.) 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.

D(x,t)=(1.0mm)sin[(2rad/m)x(200rad/s)t2)]

What is the string's displacement at x=2.5m and t=75ms?

Explanation / Answer

1) D(x,t)=(2.8cm)× sin[2(x/(6.0m)+t/(0.16s)+1)]

Put t=0.32s and x=6.5m

D(x,t)=(0.028)*sin[2(6.5/(6.0)+0.32/(0.16)+1)]= 0.014 m

2) D(x,t)=(1.0mm)sin[(2rad/m)x(200rad/s)t2)]

Put x=2.5m and t=75ms= 0.075s

D(x,t)=(0.001)sin[(2)2.5-(200)0.075-2)] = -4.78*10^-6 m

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