Equation of a standing wave is generally expressed as `y=2Asinomegatcoskx`. In the equation quantity `(omega)/(k)` represents

Options

A. the transverse speed of the particles of the string
B. the speed of either of the component waves
C. the speed of the standing wave
D. a quantity that is independent of the properties of the string.

Answer

B

Explanation

Equation of the component waves are:
`y=Asin(omegat-kx)` and `y=Asin(omegat+kx)`
where `omegat-kx=`constant or `omegat+kx=`constant
Differentiating w.r.t. `t` we get
`omega-k(dx)/(dt)=0` and `omega+k(dx)/(dt)=0`
`impliesv=(dx)/(dt)=(omega)/(k)` and `v=-(omega)/(k)`
the speed of component waves is `(omega)/(k)`