The displacement $y$ of a particle in a medium can be expressed as $y=10^{-6} \sin (100 t+20 x+\pi / 4)$ m, where $t$ is in seconds and $x$ in meter. The speed of the wave is

JEE Main · 2004 · 24 Apr 2004 · Offline · Waves & Sound

The displacement

y

of a particle in a medium can be expressed as

y = 1 0^{- 6} sin (100 t + 20 x + π /4)

m, where

t

is in seconds and

x

in meter. The speed of the wave is

Answer: (B)

For a travelling wave of the form

y = A sin (ω t + k x + ϕ)

the speed is the angular frequency divided by the wave number,

v = ω / k

. Reading off

ω = 100 s^{- 1}

and

k = 20 m^{- 1}

gives

v = 100/20 = 5 m/s

. The

+ k x

sign merely tells us the wave advances along

- x

; it has no bearing on the magnitude of the speed.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option