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Equation of a standing wave is expressed...

Equation of a standing wave is expressed as `y = 2A sinomegat coskx`. In the equation, quantity `omega//k` represents

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.

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of the component waves are `:`
`y=A sin (omegat-kx)` and `y=A sin (omegat+kx)`
where `, omegat-kx=` constant or `omegat+kx=` constant
Differentiating `w.r.t. 't':`
`omega-k(dx)/(dt)=0` and `omega +k(dx)/(dt)=0`
`rArr v=(dx)/(dt)=(omega)/(k)` and `v=-(omega)/(k)`
`i.e.,` the speed of component waves is `((omega)/(k))`
Hence `(B)`
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