When a wave travels in a medium, displacement of a particle is given by y=a sin 2 π(b t-c x), where, a, b and c are constants. The maximum particle velocity will be twice the wave velocity if

Question

When a wave travels in a medium, displacement of a particle is given by y=a sin 2 π(b t-c x), where, a, b and c are constants. The maximum particle velocity will be twice the wave velocity if (A) b=a c (B) b=(1/a c) (C) c=π a (D) (1/π a )

Tardigrade Admin · Accepted Answer

From given equation V text particle =ω x =2 π ba wave velocity =(ω/K)=(2 π b/2 π c)=(b/c) V P =2 V w 2 π ba =(2 b / c ) c=(1/π a)

Q. When a wave travels in a medium, displacement of a particle is given by $y = a sin 2 π (b t - c x),$ where, $a, b$ and c are constants. The maximum particle velocity will be twice the wave velocity if

$b = a c$

$b = \frac{1}{a c}$

$c = πa$

$\frac{1}{πa}$

From given equation
$V_{particle} = ω x = 2 πba$
wave velocity
$= \frac{ω}{K} = \frac{2 πb}{2 π c} = \frac{b}{c}$
$V_{P} = 2 V_{w}$
$2 πba = \frac{2 b}{c}$
$c = \frac{1}{πa}$

Q. When a wave travels in a medium, displacement of a particle is given by y=asin2π(bt−cx), where, a,b and c are constants. The maximum particle velocity will be twice the wave velocity if

b=ac

b=ac1​

c=πa

πa1​