1) A wave pulse propogating on a guitar string is defined by the wavefunction y(

Question

1)      A wave pulse propogating on a guitar string is defined by the wavefunction y(x,t) = 2.0/[(x-3t)2+1]  

The string has a length of 12m, and is attached to a wall on each end.  Calculate the transverse velocity (magnitude AND direction) of a point 3.0 m from the left end of the string at the following times:

a) 0.5 sec,  b) 1.0 sec  c) 2.0 sec

Hints:  

A:  This is the same wave pulse we graphed in class on the old-school TI-83 calculator.  Take a look at the pulse at 0 sec, 0.5 sec, 1 sec, and 2 sec.  Sketch those graphs.

B:  How do you find velocity when given position?  How do we find this when velocity is a function of two variables?  

C:  Be sure to label the direction on your answers! Hint:  the direction of transverse velocity isn

Explanation / Answer

the amplitude of the wave is

A = 2.0 m

the speeds are

v1 = (2.0/0.5) = 4 m/s,

v2 = (2.0/1.0) = 2 m/s

and v3 = (2.0/2.0) = 1 m/s

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