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The two strings above are stretched under a tension of 700 N. The string on the left has a linear mass density of u1 = 0.003 kg/m, and the string on the right has a linear mass density of u2 = 0.020kg/m. Let the incident wave have an amplitude of Ai = 0.5 mm and a frequency of f = 1200 Hz.
a) What are the wave speeds v1 and v2 of the re?ected and transmitted waves, in m/s?
b) What are the wavelengths ?r and ?t of the re?ected and transmitted waves, in m?
c) What is the refractive index n=k2/k1=v1/v2?
d) What are the amplitudes Ar and At of the re?ected and transmitted waves, in mm? Is either of these waves inverted?
e) What are the average powers Pi , Pr , and Pt of the incident, re?ected, and transmitted waves, in W?
f ) Note that the total average power entering the discontinuity is Pi , while the total average power leaving the discontinuity is Pr + Pt . How does the total power entering compare with the total power leaving?
My attempt:
a) V1=v (T/u1)
V2=v (T/u2)
b)wavelength reflected= speed/frequency
c)refractive index=n=v1/v2
d)Reflected wave
Amplitude=(vu1-vu2)/(vu1+vu2)
Transmitted wave
Amplitude= 2(vu1)/(vu1+vu2)
e) Pi=1/2 u v w^2 A^2
Pr=1/2 u v w^2 A^2
Pt=1/2 u v w^2 A^2
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