The standing wave in a medium is expressed as y=0.2 sin (0.8 x) cos (3000 t) m. The distance between any two consecutive points of minimum or maximum displacement is

Question

The standing wave in a medium is expressed as y=0.2 sin (0.8 x) cos (3000 t) m. The distance between any two consecutive points of minimum or maximum displacement is (A) (π/2) m (B) (π/4) m (C) (π/6) m (D) None of these

Tardigrade Admin · Accepted Answer

y=0.2 sin 0.8 x cos 3000 t The distance between any two points of minimum or maximum displacement is simply wavelength ((λ/4)) of the wave. k=(2 π/λ)=0.8 or λ=(2 π/0.8) ∴ λ=(5 π/2) m ⇒ (λ/4)=(5 π/8) m

Q. The standing wave in a medium is expressed as $y = 0.2 sin (0.8 x) cos (3000 t) m$ . The distance between any two consecutive points of minimum or maximum displacement is

$\frac{π}{2} m$

$\frac{π}{4} m$

$\frac{π}{6} m$

None of these

$y = 0.2 sin 0.8 x cos 3000 t$
The distance between any two points of minimum or maximum displacement is simply wavelength $(\frac{λ}{4})$ of the wave.
$k = \frac{2 π}{λ} = 0.8$
or $λ = \frac{2 π}{0.8}$
$∴ λ = \frac{5 π}{2} m$
$\Rightarrow \frac{λ}{4} = \frac{5 π}{8} m$

Q. The standing wave in a medium is expressed as y=0.2sin(0.8x)cos(3000t)m. The distance between any two consecutive points of minimum or maximum displacement is

2π​m

4π​m

6π​m