Question

# The transverse wave propagating through a medium is given by $$y=A\cos { 2\pi } \left[ ft-\cfrac { x }{ \lambda } \right]$$. If maximum particle velocity of medium is two times the velocity of wave through medium, then.

A
λ=3.14A
B
λ=6.28A
C
6.28λ=A
D
3.14λ=A

Solution

## The correct option is A $$\lambda =3.14A$$Velocity of a particle $${{v}_{p}}=\nu \lambda$$ $${{v}_{p}}=A\omega$$ $$=A2\pi \nu .....(1)$$ Maximum velocity of a wave $${{v}_{g}}=\nu \lambda ............(2)$$ It is given that $${{v}_{p}}=2{{v}_{g}}$$ Using equation (1) and (2) $$A2\pi \nu =2\nu \lambda$$ $$\lambda =\pi A$$ $$\lambda =3.14\,A$$ Physics

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