A transverse mechanical harmonic wave is travelling on a string. Maximum velocity and maximum acceleration of a particle on the string are `3m//s` and `90 m//s^(2)`, respectively. If the wave is travelling with a speed of `20 m//s` on the string, write wave function describing the wave. \

Explanation

Maximum particle velocity, `mu_(max)=omegaA`
`Maximum particle acceleration, `a_max=omega^(2)A`
dividing eq. (ii) by eq.(i)
`:.`Angular frequency, `omega=(a_(max)/(mu_max)=(90)/(3)=30 rad//s`
From Eq.(i), amplitude, `A=(mu_max)/(omega)=(3)/(30)=0.1 m`
propagation constant, `k(omega)/(v) (30)/(20) 1.5 m^(-1)`
Equation of wave of wave is `y+A sin(omegat+-kx)`
or wave function `y=0.1 sin (30t+-1.5x)`
`Where x is in metres and t in seconds.
Positive sign is for wave propagation along negative `x-`axis and negative sing for wave propagating along positive `x-`axis.