A wave is expressed by the equation y=0.5 sin π(0.01 x-3 t), where x, y are in metres and t in seconds. The speed of propagation will be

Question

A wave is expressed by the equation y=0.5 sin π(0.01 x-3 t), where x, y are in metres and t in seconds. The speed of propagation will be (A) 300 m/s (B) 150 m/s (C) 250 m/s (D) 450 m/s

Tardigrade Admin · Accepted Answer

The standard equation of wave of amplitude

a

is

y = a sin (k x - ω t)

... (i)
where

ω

is angular velocity.
Given equation is

y = 0.5 sin (0.01 π x - 3 π t)

...(ii)
Comparing Eqs. (i) and (ii), we get

k = 0.01 π, ω = 3 π

k = \frac{ω}{v}

\Rightarrow v = \frac{ω}{k} = \frac{3 π}{0.01 π} = 300 m / s

Q. A wave is expressed by the equation y=0.5sinπ(0.01x−3t), where x,y are in metres and t in seconds. The speed of propagation will be

300 m/s

150 m/s

250 m/s

450 m/s

The standard equation of wave of amplitude a is y=asin(kx−ωt) ... (i) where ω is angular velocity. Given equation is y=0.5sin(0.01πx−3πt)...(ii) Comparing Eqs. (i) and (ii), we get k=0.01π,ω=3π k=vω​ ⇒v=kω​=0.01π3π​=300m/s

Q. A wave is expressed by the equation $y = 0.5 sin π (0.01 x - 3 t)$ , where $x, y$ are in metres and $t$ in seconds. The speed of propagation will be