Two string tied together have different linear mass densities and hence differen

Question

Two string tied together have different linear mass densities and hence different velocities. Reflection and transission coefficient in terms of amplitude:

a) supposed string 1 is a thick string and string 2 is thin. in which string is the speed larger?

b) What are R and T in the limit of v1 << v2?

c) What are R and T in the limit of v1 >> v2?

d) the power carried by a wave in a strong was found to be

u0 is maximum transverse particle speed, T and mu are the tension and the linear density for the string, and v is the speed of the wave. u0 = wA, A being amplitude

Tpower = Power transmitted / power incident

e) what is Rpower + Tpower?

Explanation / Answer

a) Speed in string 2 will be larger.

b) R = 1 , T = 2

c) R = -1 , T = 0

d)

e) Rpower + Tpower = ( ( 3*v2 - v1 ) * - ( v2 + v1 ) ) / ( v2 + v1 )^2

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