A harmonically moving transverse wave on a string has a maximum particle velocity and acceleration of 3 m/s and `90 m//s^(2)` respectively. Velocity of the wave is `20 m//s`. Find the waveform.

Options

A. `y = 0.5 sin (20 t + 1.5x)`
B. `y = 0.1 sin (30 t + 1.5x)`
C. `y = 0.1 sin (40 t + 2x)`
D. `y = 0.2 sin (30 t + x)`

Answer

B

Explanation

`v_("max") = A omega = 3m//s` ….(1)
`a_("max) = A omega^(2) = 90 m//s^(2)`….(2)
`:. omega = (A omega^(2))/(A omega) = (90)/(3) = 30` rad/s
and `A = ((A omega)^(2))/(A omega^(2)) = (9)/(90) = 0.1m`
`:' v = (omega)/(K) :. K = (omega v) = (30)/(20) = 1.5`
`:.` The equation of the waveform is
`y = A sin (omega t + Kx) = 0.1 sin (30t + 1.5 x)`