The harmonic wave `y_i = (2.0 xx 10^(-3)) cos pi (2.0x - 50t)` travels along a string towards a boundary at x=0 with a second string. The wave speed on the second string is `50 m//s`. Write expressions for reflected and transmitted waves. Assume SI units.

Answer

(i) `6.67 xx 10^(-4) pi (2.0 x+50 t)`
(ii) `2.67 xx 10^(-3) cos pi(1.0 x - 50 t)`

Explanation

Amplitude of reflected wave
`A_(r)=A_(i)((k_(2)-k_(1))/(k_(2)+k_(1)))=2((25-50)/(25+50))xx10^(-3)`
`=0.667xx10^(-3)=6.67xx10^(-4)`
Amplitude of transmitted wave
`A_(1)=((2k_(1))/(k_(1)+k_(2)))A_(1)=(2xx50xx2)/(50+25)xx10^(-3)`
`=2.67 xx10^(-3)`
`:.` Equation of reflected wave
`y_(1)=6.67xx10^(-4)cospi(2x+50t)`
Equation of transmitted wave
`y_(1)=2.67xx10^(-3)cospi(x-50t)`