A sinusoidal wave on a string is described by the wave function where x and y are in metres and t is in seconds. The mass per unit length of this string is `12.0 g//m`. Determine (a) the speed of the wave, (b) the wavelength, (c ) the frenquecy and (d) the power transmitted to the wave.

Explanation

Comparing the given wave function,
`y=(0.15 m0sin (0.80x-50r)`
with the general wave function,
`y=A sin (ks-omegat)`
We have k`=0.80 rad//m` and `omega=50 rad//s and A=0.15 m`
`(a) the wave speed is then
`v=flambda=(omega)/(k)=(50.0 rad//s)/(0.80 rad//m)=62.5 m//s`
(b) The wavelength is
lambda=(2pi)/(k)=(2pi rad)/(0.80 rad/m)=7.85 m`
(c ) The frequency is
`f (omega)/(2pi) (50 rad//s)/(2pi and) 7.96 Hz`
(d) The wave carries power
`pmu(1)/(2)muomega^(2)A^(2)v`
`mu(1)/(2)(0.0120 kg//m)(50.0 s^(-1))^(2)(0.150 m)^(2)(62.5 m//s)`
`mu21.1 W`