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Find the wrong statement from the following about the equation of stationary wave given by `Y = 0.04 cos(pix) sin(50 pit)` m where tis in second. Then for the stationary wave.A. Time period= 0.02 sB. Wavelength= 2 mC. Velocity = 50 m/sD. Amplitude= 0.02 m |
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Answer» Correct Answer - A The given equation of wave is ` " " y= 0.04cos (pix ) sin ( 50 pit ) ` `=0.02sin (50pit + pix ) +0.02sin ( 50pi t -nx )` ` " "[because 2sin A *cos B =sin (A+B)_ *cos (A-B) ]` Thus the given wave is the combination of two waves, ` y_1 =0.02sin ( 50pi t + pix) " " ` (in -ve x - direction ) and ` y _2 =0.02sin (50 pit -npi ) " " ` (in + ve x- direction ) Comparing them the general equation of wave a ` sin (omega t +kx) ` ,we get Amplitude ` " "a= 0.02m ` time period ` " "T = (2pi)/( 50 pi ) =(1)/(25) =0.04s ` Wavelength `lambda =(2pi)/( pi) =2m ` velocity , `v =( 50 pixxlambda )/(2pi) ` ` " "= ( 100 )/(2) =ms^(-1) ` So, option (a) is wrong |
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