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A standing wave is formed by two harmonic waves, `y_1 = A sin (kx-omegat) and y_2 = A sin (kx + omegat)` travelling on a string in opposite directions. Mass density energy between two adjavent nodes on the string. |
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Answer» Correct Answer - A::B The distance between two adjacent nodes is ` lambda/2 or pi/k.` `:. Volume of string between two nodes will be ` `V = ("area of cross-section") xx ("distance between two nodes")` `=(S) (pi/k)` Energy density (energy per unit volume) of a travelling wave is given by `u=1/2 rho A^2 omega^2` A standing wave is formed by two identical waves travelling in opposite directions. Therefore, the energy stored between two nodes in a standing wave. `E= 2`[energy stored in a distance of `pi/k` of a tracelling wave] = 2 (energy density)(volume) = 2 (1/2 rho A^2 omega^2) ((piS)/k) or `E = (rho A^2 omega^2 piS)/k` |
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