A wave y=a\sin \left ( \omega t-kx \right ) on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is :

  • Option 1)

    y=a\sin \left ( \omega t+kx \right )

  • Option 2)

    y=-a\sin \left ( \omega t+kx \right )

  • Option 3)

    y=a\sin \left ( \omega t-kx \right )

  • Option 4)

    y=-a\sin \left ( \omega t-kx \right )

 

Answers (1)

As we learnt in

Property of stationary waves -

1)    Disturbance do not move in any direction.

2)    All particles except nodes perform S.H.M.

3)    During the formation of a stationary wave the medium is broken into equally spaced loops

4)    Amplitude of the particle is different at different point

 

-

 

 

 

:    Consider option (a)

Stationary wave :

Y=a\sin \left ( \omega t+kx \right )+a\sin \left ( \omega t-kx \right )

when x=0,    Y is not zero. The option is not acceptable.

Consider option (b)

Stationary wave :

Y= a\sin \left ( \omega t-kx \right )-a\sin \left ( \omega t+kx \right )

At x= 0,Y= a\sin \omega t -a\sin \omega t= 0

This option holds good

Option (c) givesY= 2a\sin\left ( \omega t -kx \right )

At x=0,Y\neq 0

Option (d) gives Y = 0

Hence only option (b) holds good

Correct option is 2.


Option 1)

y=a\sin \left ( \omega t+kx \right )

This is an incorrect option.

Option 2)

y=-a\sin \left ( \omega t+kx \right )

This is the correct option.

Option 3)

y=a\sin \left ( \omega t-kx \right )

This is an incorrect option.

Option 4)

y=-a\sin \left ( \omega t-kx \right )

This is an incorrect option.

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