A plane progressive harmonic wave is given by the equation: ϕ=ϕmsin(2t−3x+4y+π/3), where x and y are in meters, and t is in seconds. Let n^ be the unit vector in the direction of wave propagation, and v is the speed of wave with respect to medium, then: -

n ^ = − 3 5 i ^ + 4 5 j ^ ; v = 0.4 m / s

A plane progressive harmonic wave is given by the equation: ϕ=ϕmsin(2t−3x+4y+π/3), where x and y are in meters, and t is in seconds. Let n^ be the unit vector in the direction of wave propagation, and v is the speed of wave with respect to medium, then: -

n ^ = − 3 5 i ^ + 4 5 j ^ ; v = 0.4 m / s

n ^ = − 4 5 i ^ + 3 5 j ^ ; v = 0.5 m / s

n ^ = 4 5 i ^ − 3 5 j ^ ; v = 2 3 m / s

n ^ = − 3 5 i ^ + 4 5 j ^ ; v = 0.4 m / s

n ^ = 3 5 i ^ − 4 5 j ^ ; v = 0.4 m / s

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A plane progressive harmonic wave is given by the equation: $ϕ = ϕ_{m} \sin (2 t - 3 x + 4 y + π / 3)$ , where x and y are in meters, and t is in seconds. Let $\hat{n}$ be the unit vector in the direction of wave propagation, and v is the speed of wave with respect to medium, then: -

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$\hat{n} = - \frac{4}{5} \hat{i} + \frac{3}{5} \hat{j}; v = 0.5 m / s$

$\hat{n} = \frac{4}{5} \hat{i} - \frac{3}{5} \hat{j}; v = \frac{2}{3} m / s$

$\hat{n} = - \frac{3}{5} \hat{i} + \frac{4}{5} \hat{j}; v = 0.4 m / s$

$\hat{n} = \frac{3}{5} \hat{i} - \frac{4}{5} \hat{j}; v = 0.4 m / s$

answer is C.

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Detailed Solution

$ϕ = ϕ_{m} \sin (2 t - (3 x - 4 y) + π / 3)$

$\hat{n}$ will be along the normal to plane
$\hat{n} = \frac{3 \hat{i} - 4 \hat{j}}{5}$
In general, $a x + b y + c z + d = 0$
$\hat{n}$ will be along $a \hat{i} + b \hat{j} + c \hat{k}$
Wave speed $= \frac{w}{k} = \frac{2}{5} = 0.4 m / s$

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