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.

Answer

A, B

Explanation

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`