Potential energy of transversal and longitudinal wave

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Mechanical waves are classified into transversal and longitudinal types, each having distinct methods for calculating potential energy. For longitudinal waves, potential energy can be calculated using a spring model with the formula 1/2 k' x'^2. In contrast, potential energy for transversal waves involves integrating T sine theta dy, although the exact approach may need clarification. Both types involve oscillators moving around equilibrium positions, with transversal waves oscillating vertically and longitudinal waves oscillating horizontally. Understanding these differences is crucial for accurately calculating potential energy in wave mechanics.
k.soedyatmiko
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We have 2 kind of mechanical wave, which is transversal and longitudinal. In calculating the kinetic energy we just integrate dm v^2 of course. Also in calculating the potential energy of an element of a longitudinal wave we can do it by making it as a small spring with a constant k' and just count 1/2 k' x'^2. But how we count the potential energy of a transversal wave. I have tried to integrate T sine theta dy, but I think that's not how we do that. I do need helps from all of you. Thanks. Sorry about my English.
 
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You calculate it the same way. In the transverse case you have a whole bunch of oscillators moving vertically up and downrelative to a horizontal equilibrium line; in a longitudinal wave you have a whole bunch of oscillators moving horizontally back and forth relative to vertical equilibrium lines.
 

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