A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is `3m//s` and maximum transverse acceleration is `90m//s`. If the wave velocity is `20 m//s` then find the waveform.

Explanation

Here, `v_(max)=omegar=3ms^(-1)` ...(i)
`a_(max)=omega^(2)r=90ms^(-2)`
velocity of wave, `v=(omega)/(k)=20ms^(-1)`
`(a_(max))/(v_(max))=(omega^(2)r)/(omegar)=(90)/(3):.omega=30rad//s`
From (i), `r=(3)/(omega)=(3)/(30)=0.1m`
From `v=(omega)/(k)=20,k=(omega)/(20)=(30)/(20)=1.5rad//s`
`:.` The equation of waveform is
`y=rsin(omegat+kx)=0.1sin(30t+1.5x)`