InterviewSolution
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InterviewSolution
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For the travelling harmonic wave `y ( x,t) = 2.0 cos 2pi``( 10t- 0.0080x+0.35)` where x and yare in cm and t in s. Calculate the phase differencebetween oscillatory motion of two points separated by a distance of a) 4m, (b) 0.5m (c ) `lambda //2` (d) `3lambda //4` |
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Answer» The given equation be written as `y =2.0 cos [ 2p( 10t-0.0080x) + 2pi xx0.35]` `y =2.0 cos[ 2pi xx 0.0080 ((10t)/(0.0080) -x)+ 0.7 pi]` Compare it with the standard equation of a travelling harmonic ,we have `y =r . Cos[(2pi)/(lambda) (vt-x) + ph_(0)]` We get, `(2pi)/( lambda)= 2pixx0.0080` Further ,we know that phase diff. `phi=( 2pi)/( lambda) x ` (a) Whe `x = 4m= 400 cm ` `phi =( 2pi)/(lambda).x =2pixx0.0080xx400` `= 6.4 pi rad.` (b) When`x =0.5=50 cm` `phi= ( 2pi)/( lambda ) .x = 2pixx0.0080 xx50` `= 0.8 pi ` rad. (c ) When `x = ( lambda)/(2)` `phi = ( 2pi)/( lambda) xx( lambda )/(2)= pi`rad. (d) When `x= (3 lambda)/( 4)` `phi = ( 2pi)/( lambda) xx ( 3 lambda)/( 4) = ( 3lambda)/(2)` rad. |
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