The equation of a wave is $y = 4 \sin [\frac{π}{2} (2 t + \frac{1}{8} x)]$ where y and x are in cm and t is in second

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Two position occupied by the particle at separation of 12 cm have a phase difference of 135°

The amplitude, wavelength, velocity and frequency of wave are $4 cm, 32 cm, 16 cm / s, and 0.5 Hz$ respectively with wave propagating along -x direction

Two position occupied by the particle at time interval of 0.4 s have a phase difference of 0.4 $π$ radian

The amplitude, wavelength, velocity and frequency of wave are 4 cm, 16 cm, 32 cm^-1 and 1 Hz re spectively with wave propagating along +x direction

answer is B, C, D.

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Detailed Solution

$y = 4 \sin [\frac{π}{16} (16 t + x)]$ it is compare with
$y = asin (\frac{2 π}{λ} (Vt + x))$

The amplitude, wavelength, velocity and frequency of wave are $4 cm, 32 cm, 16 cm / s, and 0.5 Hz$ respectively with wave propagating along -x direction
Also $Δϕ = \frac{2 π}{λ} . (Δx) \Rightarrow Δϕ = \frac{2 π}{λ} (V \cdot Δt)$