Wave Reflection at an Impedance Discontinuity The impedance for mechanical waves is defined as the ratio between the force wave and velocity wave and in general takes the for For transverse waves in a string with linear mass density If two strings with different mass densities are connected with a common tension, the impedance discontinuity at the joint causes wave reflection. For an incident displacement wave of unit amplitude in string 1, the reflected wave is and transmitted wave is The first animation shows reflection and transmission of incident pulse wave of unit amplitude when the mass density ratio is 4, Z1/Z2 = 1/2. The reflected wave is negative and its peak is -1/3. The transmitted wave, which propagates slower, has an amplitude of 1 - 1/3 = +2/3, as expected from the formulae. When Z_1/Z_2 = 2.0. > with(plots): When Z_2 = infinity. (Fixed end) > with(plots): When Z_2 = 0. (Free end) > animate((exp(-(x-t)^2)+exp(-(x+t)^2)),x=-10..0,t=-10..10,frames=50,color=red,numpoints=200); |
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