A wave motion is described by y(x, t) = a sin (kx - ω t). Then the ratio of the maximum particle velocity to the wave velocity is

Question

A wave motion is described by y(x, t) = a sin (kx - ω t). Then the ratio of the maximum particle velocity to the wave velocity is (A) ka (B) (ω/k) (C) (d ω/dk) (D) (x/l)

Tardigrade Admin · Accepted Answer

Maximum particle velocity (vp)max = a ω an wave velocity, v = (ω/k) ∴ Ratio ((vp)max/v) = (a ω k/ω) = ka

Q. A wave motion is described by $y (x, t) = a sin (k x - ω t)$ .
Then the ratio of the maximum particle velocity to the wave velocity is

ka

$\frac{ω}{k}$

$\frac{d ω}{d k}$

$\frac{x}{l}$

Maximum particle velocity $(v_{p})_{ma x} = aω$ an wave velocity, $v = \frac{ω}{k}$
$∴ R a t i o \frac{( v _{p} ) _{ma x}}{v} = \frac{aωk}{ω} = ka$

Q. A wave motion is described by y(x,t)=asin(kx−ωt). Then the ratio of the maximum particle velocity to the wave velocity is

ka

kω​

dkdω​

lx​

Maximum particle velocity (vp​)max​=aω an wave velocity, v=kω​ ∴Ratiov(vp​)max​​=ωaωk​=ka

Q. A wave motion is described by $y (x, t) = a sin (k x - ω t)$ .
Then the ratio of the maximum particle velocity to the wave velocity is

$\frac{ω}{k}$

$\frac{d ω}{d k}$

$\frac{x}{l}$

Maximum particle velocity $(v_{p})_{ma x} = aω$ an wave velocity, $v = \frac{ω}{k}$
$∴ R a t i o \frac{( v _{p} ) _{ma x}}{v} = \frac{aωk}{ω} = ka$