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

Question

When a wave travels in a medium the particles displacement is, given by the equation y=0.03 sin π(2t-0.01 x), where x and y 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

Here, displacement equation is y=0.03 sin π(2 t-0.01 x) ...(i) The standard equation is y=a sin 2 π((t/T)-(x/λ)) ...(ii) Comparing the given Eq. (i) with standard Eq. (ii), we have (2/λ)=0.01 or λ=(2/0.01)=200 m

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

200 m

100 m

20 m

10 m

Here, displacement equation is
$y = 0.03 sin π (2 t - 0.01 x)$ ...(i)
The standard equation is
$y = a sin 2 π (\frac{t}{T} - \frac{x}{λ})$ ...(ii)
Comparing the given Eq. (i) with standard Eq. (ii), we have
$\frac{2}{λ} = 0.01$
or $λ = \frac{2}{0.01} = 200 m$

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