If equation of transverse wave is y=x0 cos 2 π(n t-(x/λ)). Maximum velocity of particle is twice of wave velocity, if λ is-

Question

If equation of transverse wave is y=x0 cos 2 π(n t-(x/λ)). Maximum velocity of particle is twice of wave velocity, if λ is- (A) π / 2x0 (B) 2λ x0 (C) π x (D) π x0

Tardigrade Admin · Accepted Answer

y=x0 cos 2 π(n t-(x/λ)) y=x0 cos (2 π/λ)(v t-x) [∴ v=n λ] ((d y/d t)) max =x0 × (2 π/π) v=2 v (given) ∴ λ=π x0

Q. If equation of transverse wave is $y = x_{0} cos 2 π (n t - \frac{x}{λ})$ . Maximum velocity of particle is twice of wave velocity, if $λ$ is-

$π /2 x_{0}$

$2 λ x_{0}$

$π x$

$π x_{0}$

$y = x_{0} cos 2 π (n t - \frac{x}{λ})$
$y = x_{0} cos \frac{2 π}{λ} (v t - x)$
$[∴ v = nλ]$
$(\frac{d y}{d t})_{m a x} = x_{0} \times \frac{2 π}{π} v = 2 v$ (given)
$∴ λ = π x_{0}$

Q. If equation of transverse wave is y=x0​cos2π(nt−λx​). Maximum velocity of particle is twice of wave velocity, if λ is-

π/2x0​

2λx0​

πx

πx0​