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A sinusoidal wave of amplitude A1 approaches a and travels through a region of the string in which the mass per unit length changes gradually from mu_1 to mu_ 2. It can be shown that , in such a situation, there is no reflection provided the distance over which the change occurs is large compared with the wavelength. On this assumption , show that final amplitude A 2 is given by

(A1/A2)=(mu_1/mu_2)^(1/4)

 

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