The equation of a simple harmonic wave is given by y = 6 Sin 2π(2t - 0.1x), where x and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is

Question

The equation of a simple harmonic wave is given by y = 6 Sin 2π(2t - 0.1x), where x and y are in mm and t is in seconds. The phase difference between two particles 2 mm apart at any instant is (A) 18° (B) 36° (C) 54° (D) 72°

Tardigrade Admin · Accepted Answer

From the given equation k=0.2 π ⇒ (2 π/λ) =0.2 π ⇒ λ =10 mm Δ φ =(2 π/λ) Δ x=(2 π/10) × 2=(2 π/5)=72°

Q. The equation of a simple harmonic wave is given by $y = 6 S in 2 π (2 t - 0.1 x)$ , where $x$ and $y$ are in $mm$ and $t$ is in seconds. The phase difference between two particles $2 mm$ apart at any instant is

18 $^{\circ}$

36 $^{\circ}$

54 $^{\circ}$

$7 2^{\circ}$

From the given equation $k = 0.2 π$
$\Rightarrow \frac{2 π}{λ} = 0.2 π$
$\Rightarrow λ = 10 mm$
$Δ ϕ = \frac{2 π}{λ} Δ x = \frac{2 π}{10} \times 2 = \frac{2 π}{5} = 7 2^{\circ}$

Q. The equation of a simple harmonic wave is given by y=6Sin2π(2t−0.1x), where x and y are in mm and t is in seconds. The phase difference between two particles 2mm apart at any instant is

18∘

36∘

54∘

72∘