Question

a plane wave is described by the eqn 'y=3cos(x/4-10t-pi/2).the maxm velocty of the particles of the medium due to this wave is??

Answer 1

hope u understand the calculations yourself

Answer 2

maximum velocity of particle is 30

a plane wave is described by the equation, y = 3cos(x/4 - 10t - π/2)

To find velocity, differentiate y with respect to t,

dy/dt = 3 d{cos(x/4 - 10t - π/2)}/dt

= 3 {-10sin(x/4 - 10t - π/2)}

= -30sin(x/4 - 10t - π/2)

here negative value is included. it means to get maximum velocity, we have to put minimum value of sin(x/4 - 10t - π/2), haven't we ?

now tell me what is the minimum value of sine function ?, of course, -1.

so, maximum velocity of particle, v = -30 × -1 = 30

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