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.

Options

A. Time period= 0.02 s
B. Wavelength= 2 m
C. Velocity = 50 m/s
D. Amplitude= 0.02 m

Answer

A

Explanation

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