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Unformatted text preview: Physics 218 Spring 2008 1 Traveling Wave on a Loaded String We found that the general solution for the p th mass on a traveling wave is y p ( t ) = C sin[ p n N + 1 ] cos n t y ( x, t ) = C sin[ n L x ] cos n t where x pl , L = ( N + 1) l and n is the n th mode of the system. Lets concentrate on the second version - the continuous version which will be more interesting for N large and l small. We want to show that this is of the form f ( x vt ), as this is of the form of a traveling wave. Recall that 2 sin a cos b = sin( a + b ) + sin( a- b ). We can recast our equation in that form. y p ( t ) = C 2 h sin( n L x- n t ) + sin( n L x + n t ) i Look at n- we want to factor out n L . 2 n = 4 2 sin 2 1 2 n N + 1 Remember that 2 = T ml and L = ( N + 1) l . Lets consider the physical case where we have lots of masses on our string ( N large) and we are looking at a low mode ( n small). Then n N + 1 1 and we can rewrite the sin 2 x x...
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