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Standard XII

Physics

Principle of Superposition

Two particles...

Question

Two particles of medium disturbed by the wave propagation are at $x_{1} = 0$ and $x_{2} = 1 c m$ . The respective displacements (in $c m$ ) of the particles can be given by the equations :
$y_{1} = 2 sin 3 π t, y_{2} = 2 sin (3 π t - π / 8)$
The wave speed is

16 c m / s e c

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24 c m / s e c

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12 c m / s e c

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8 c m / s e c .

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Solution

The correct option is B $24 c m / s e c$
$Given ω = 3 π, ϕ = \frac{π}{8}, Δ x = 1 x$
$f = \frac{ω}{2 π} = \frac{3 π}{2 π} 2 = 1.5$
$ϕ = \frac{2 π}{λ} Δ x$
$\Rightarrow \frac{π}{8} = \frac{2 π}{λ} \times 1$
$\Rightarrow λ = 16 cm$
$v = f λ = 1.5 \times 16 = 24 cm/sec$

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[CPMT 1986]

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Two particles of medium disturbed by the wave propagation are at x1=0 and x2=1cm. The respective displacements (in cm) of the particles can be given by the equations :y1=2sin3πt,y2=2sin(3πt−π/8)The wave speed is

The correct option is B 24cm/secGivenω=3π,ϕ=π8,Δx=1 x f=ω2π=3π2π2=1.5ϕ=2πλΔx⇒π8=2πλ×1⇒λ=16 cmv=fλ=1.5×16=24 cm/sec

Two particles of medium disturbed by the wave propagation are at $x_{1} = 0$ and $x_{2} = 1 c m$ . The respective displacements (in $c m$ ) of the particles can be given by the equations :
$y_{1} = 2 sin 3 π t, y_{2} = 2 sin (3 π t - π / 8)$
The wave speed is

The correct option is B $24 c m / s e c$
$Given ω = 3 π, ϕ = \frac{π}{8}, Δ x = 1 x$
$f = \frac{ω}{2 π} = \frac{3 π}{2 π} 2 = 1.5$
$ϕ = \frac{2 π}{λ} Δ x$
$\Rightarrow \frac{π}{8} = \frac{2 π}{λ} \times 1$
$\Rightarrow λ = 16 cm$
$v = f λ = 1.5 \times 16 = 24 cm/sec$