The transverse wave in a string is represented by `y ( x,t) = 7.5 sin (12 pi t - 0.005 x ) ` where 'x' and 'y' in cm and 't' in second. Determine ( a) Amplitude (b) frequency (c ) wavelength and ( d) velocity of the wave.

Explanation

The given equation is in the form `y = A sin (omega t - kx ) `.
On comparing , `A =7.5 cm = 7.5 xx 10^(-2) m`
`omega = 12pi rads^(-1 )` and `omega = 2pi f `
Therefore,` f = ( 12 pi )/(2pi ) = 6Hz`.
Also, `k =0.005 rad cm^(-1) = 0.5 rad m^(-1)`
`lambda =( 2pi )/( k ) = ( 2 xx 3.142 ) /( 0.005 ) = 1.256 xx 10^(3) cm = 12.56m`
Wave velocity `v = ( omega )/(k ) =(12 xx 3.142)/(0.005 ) =7.54 xx 10^(3) cms^(-1) = 75.41 ms^(-1)`