A wave travels in a medium according to the equation of displacement given by y( x, t) = 0.03 sin π (2t - 0.01 x) where y and x are in metre and t in second. The wavelength of the wave is

Question

A wave travels in a medium according to the equation of displacement given by y( x, t) = 0.03 sin π (2t - 0.01 x) where y and x are in metre and t in second. The wavelength of the wave is (A)  200 m  (B)  100 m  (C)  20 m  (D)  10 m

Tardigrade Admin · Accepted Answer

Comparing the given equation with standard wave equation we find that the propagation constant k =(π × 0.01) m -1 ∴ Wavelength λ =(2 π/k) =(2 π/π × 0.01)=200 m

Q. A wave travels in a medium according to the equation of displacement given by
$y (x, t) = 0.03 sin π (2 t - 0.01 x)$
where $y$ and $x$ are in metre and $t$ in second. The wavelength of the wave is

$200 m$

$100 m$

$20 m$

$10 m$

Comparing the given equation with standard wave equation we find that the propagation constant
$k = (π \times 0.01) m^{- 1}$
$∴$ Wavelength $λ = \frac{2 π}{k}$
$= \frac{2 π}{π \times 0.01} = 200 m$

Q. A wave travels in a medium according to the equation of displacement given by y(x,t)=0.03sinπ(2t−0.01x) where y and x are in metre and t in second. The wavelength of the wave is

200m

100m

20m

10m