Two travelling waves 3 cos ( kx + ω t ) and 5 cos ( kx − ω t ) are travelling in -ve x-axis and +ve x-axis respectively on a string. The magnitude of average energy passing through a point on string p

Question

Two travelling waves 3 cos ( kx + ω t ) and 5 cos ( kx − ω t ) are travelling in -ve x-axis and +ve x-axis respectively on a string. The magnitude of average energy passing through a point on string per second for resulting wave is of the form ( k A 0 ​ ρ ω 3 S ​ ) . Calculate the value of A 0 ​ . Density of string is ρ and cross- sectional area is S.

TestHub · Accepted Answer

Resulting wave is y = 3 cos ( k x − ω t ) + 5 cos ( k x + ω t ) The instantaneous power for a wave on string ​ P = − T ( ∂ t ∂ y ​ ) ( ∂ x ∂ y ​ ) P = ​ − μ v 2 ( + 3 ω sin ( kx − ω t ) − 5 ω sin ( kx + ω t )) x ​ ( − 3 k sin ( kx − ω t ) − 5 k sin ( kx + ω t ) P = ​ μ v 2 ω k [ 9 sin 2 ( kx − ω t ) − 25 sin 2 ( kx + ω t ) ] ⟨ P ⟩ ​ = μ v 2 ω k [ 9 ⟨ sin 2 ( kx − ω t ) ⟩ − 25 ⟨ sin 2 ( kx + ω t ) ⟩ ] = ​ μ v 2 ω k [ 2 9 ​ − 2 25 ​ ] = − 8 ρ v 2 ω k = ​ 8 ρ S ( k ω ​ ) 2 ω k = − k 8 ρ Sw 3 ​ ​

Physics - Wave on String Question with Solution | TestHub

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