Q.

A plane progressive harmonic wave is given by the equation:  ϕ=ϕmsin(2t3x+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: -

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a

n^=45i^+35j^;     v=0.5m/s

b

n^=45i^35j^;   v=23m/s

c

n^=35i^+45j^;     v=0.4m/s

d

n^=35i^45j^;     v=0.4m/s

answer is C.

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Detailed Solution

ϕ=ϕmsin(2t(3x4y)+π/3)

n^  will be along the normal to plane
 n^=3i^4j^5
In general,  ax+by+cz+d=0
n^ will be along  ai^+bj^+ck^
Wave speed =wk=25=0.4m/s
 

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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: -