Sound and Wave - Wave phenomena

A string consists of two parts attached at x = 0. The right part of the string (x  0) has mass μ_r per unit length and the left part of the string (x  0) has mass  mass μ_l per unit length. The string tension is T. If a wave of unit amplitude travels along the left part of the string, as shown in the figure above, what is the amplitude of the wave that is transmitted to the right part of the string?

A. 1
B. 

C. 

D. 

E. 0

(GR9677 #80)

Solution:

A. FALSE
Amplitude = 1, if  μ_l  = μ_r  but from the picture  μ_l ≠ μ_r
Since μ_l  μ_r suggests we expect  the transmitted amplitude will be less than 1

B. FALSE
The answer suggests that the transmitted amplitude will be bigger than 1, it should be less than 1
Let μ_l = 1, μ_r = 4
A = 2 / (1 + √¼) = 2/(3/2) = 4/3

C. TRUE
The answer suggests that the transmitted amplitude will be less than 1
Let μ_l = 1, μ_r = 4
A = 2(√¼) / (1 + √¼) = 1/(3/2) = 2/3

D. FALSE
The answer suggests that A = 0, if  μ_l  = μ_r

E. FALSE
Amplitude = 0 if  μ_r → ∞

Answer: C