When a wave travels in a medium- the particle displacement is given by the equation y-asin2-bt-cx where a- b and c are constants- The maximum particle velocity will be twice the wave velocity if

Y = a sin (2π(bt cx)) = a sin (2π c(b/ct x)) This gives wave velocity = bc Particle velocity can be found by fixing the x coordinate and differentiating ...

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Standard XII

Physics

Wave Speed expression

When a wave t...

Question

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

c = \frac{1}{π a}

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c = π a

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b = a c

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b = \frac{1}{a c}

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Solution

The correct option is A $c = \frac{1}{π a}$
$y = a s i n (2 π (b t - c x))$

$= a s i n (2 π c (\frac{b}{c} t - x))$

This gives wave velocity $= \frac{b}{c}$

Particle velocity can be found by fixing the $x$ coordinate and differentiating w.r.t time.

Let $x = x_{0}$

$y = a s i n (2 π (b t - c x_{0}))$

Differentiating both sides,

$\frac{d y}{d t} = 2 a b π s i n (2 π (b t - c x_{0}))$

$\Rightarrow v_{m a x} = 2 a b π$

By putting $2 a b π = \frac{b}{c}$

$\Rightarrow c = \frac{1}{π a}$

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

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